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Co-ordinate Geometry · CAPE Pure Mathematics Unit 1

159 past-paper questions on Co-ordinate Geometry, part of Trigonometry, Geometry and Vectors, from every CAPE Pure Mathematics Unit 1 paper on Quelpr.

Practise Co-ordinate Geometry
  1. Q291 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1The line passing through the centre of the circle (x - 3)^2 + (y + 2)^2 = 25 and parallel to the x-axis, has the equation
  2. Q301 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1The curve with parametric representation x = 2t, y = t^2 has equation
  3. Q161 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The radius of the circle 2x^2 + 2y^2 - 4x + 12y + 11 = 0 is
  4. Q231 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The equation of the line passing through (0, -21) and perpendicular to x + 5y + 27 = 0 is
  5. Q241 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The equation of the circle with centre (-3, 5) and radius 6 is
  6. Q251 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1A circle has centre (-1, -1). The equation of the tangent to the circle at the point (0, -3) on the circle is
  7. Q261 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The curves y^2 = x + 7 and xy = 6 intersect in three points. The y coordinates of these points are
  8. Q271 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The curve with parametric representation x = 2t, y = t^2 has Cartesian equation
  9. 4(a)(i)4 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2A circle has equation x^2 + y^2 - 10x + 4y - 5 = 0. Determine the centre and radius of the circle.
  10. 4(a)(ii)4 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2Determine the equation of the tangent to the circle at the point (2, 3).
  11. 4(d)6 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2A point P(x, y) moves in the xy plane such that it is the same distance from the point A(1, 2) as it is from the line x = 3. Determine the equation of the locus of P.
  12. 47 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1Solve the following pair of equations simultaneously: x - 2y = -3 x^2 + 3y = 7
  13. 6(a)(i)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1Find the coordinates of M.
  14. 6(a)(ii)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1Find the gradient of the line through A and B.
  15. 6(a)(iii)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1Find the equation of the line through M and N.
  16. 6(b)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1The point P on AB divides AB internally such that the ratio AP : PB is 3 : 1. Find the coordinates of P.
  17. 6(a)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1Find the equation of the line through P and Q.
  18. 6(b)3 marks· CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1Find the coordinates of the point Q.
  19. 6(c)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1Find the EXACT length of the line segment PQ.
  20. Q231 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1The normal at P(4, 3) to the circle (x - 2)^2 + y^2 = 25 has gradient \frac{3}{4}. The equation of the tangent at P to (x - 2)^2 + y^2 = 25 is
  21. Q241 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1The line through the points P(k, 2) and Q(6, 8) is parallel to the line with equation 3x + y - 21 = 0. The value of k is
  22. Q251 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1A curve C is given by the parametric equations x = 2\sin\theta, y = \cos\theta. The Cartesian equation of C is
  23. Q161 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1The centre of the circle (x - 1)^2 + (y - 2)^2 = 16 is
  24. Q181 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1The equation of the circle whose centre has coordinates (4, 1) and whose radius is 7 units is
  25. Q251 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1A curve is defined by the parametric equations x = 3 + 2t and y = \frac{1}{t}. The Cartesian equation of the curve is
  26. Q291 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1The relationship between the curve y = x^2 - 2x + 4 and the line y = 2x is that the line
  27. Q301 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1The point (2, 3) is at one end of a diameter of the circle whose equation is x^2 + y^2 - 10x + 2y + 1 = 0. The coordinates of the other end of the diameter are
  28. Q181 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 1The circle with equation x^2 + y^2 - 2x - 4y - 11 = 0 has radius equal to
  29. Q191 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 1The equation of the circle whose centre has coordinates (4, 1) and whose radius is 7 units is
  30. Q241 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 1The curve with parametric representation x = 2t, y = t^2 has Cartesian equation
  31. Q161 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1The centre of the circle (x - 1)^2 + (y - 2)^2 = 16 is
  32. Q221 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1Which of the following equations best represents the graph?
  33. Q231 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1A curve is defined by the parametric equations x = 3 + 2t and y = \frac{1}{t}. The Cartesian equation of the curve is
  34. Q271 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1The line through the points P(k, 2) and Q(6, 8) is parallel to the line with equation 3x + y - 21 = 0. The value of k is
  35. Q301 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1The point (2, 3) is at one end of a diameter of the circle whose equation is x^2 + y^2 - 10x + 2y + 1 = 0. The coordinates of the other end of the diameter are
  36. Q191 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1The equation of the circle whose centre has coordinates (4, 1) and whose radius is 7 units is
  37. Q211 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1The point (2, 3) is at one end of a diameter of the circle whose equation is x^2 + y^2 - 10x + 2y + 1 = 0. The coordinates of the other end of the diameter are
  38. Q161 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1The centre of the circle (x - 1)^2 + (y - 2)^2 = 16 is
  39. Q221 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1The equation of the circle with centre (-3, 5) and radius 6 is
  40. Q231 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1A curve is defined by the parametric equations x = 3 + 2t and y = \frac{1}{t}. The Cartesian equation of the curve is
  41. Q261 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1The variable point P(x, y) moves so that it is the same distance from the points (1, 6) and (3, 2). The equation of the locus of P may be obtained from
  42. Q281 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1A circle has centre (-1, -1). The equation of the tangent to the circle at the point (0, -3) on the circle is
  43. Q161 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1A curve is defined by the parametric equations x = 3 + 2t and y = \frac{1}{t}. The Cartesian equation of the curve is
  44. Q181 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1The centre of the circle (x - 1)^2 + (y - 2)^2 = 16 is
  45. Q191 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1The relationship between the curve y = x^2 - 2x + 4 and the line y = 2x is that the line
  46. Q221 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1The curves y^2 = x + 7 and xy = 6 intersect at three points. The y coordinates of these points are
  47. Q251 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1A circle has centre (-1, -1). The equation of the tangent to the circle at the point (0, -3) on the circle is
  48. 4(a)5 marks· CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2Obtain the Cartesian equation of the curve given in parametric form x = 3\cos t and y = 4\sin t.
  49. 4(b)(i)5 marks· CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2Determine the centre and radius of the circle.
  50. 4(b)(ii)5 marks· CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2Determine the equation of the tangent to the circle at the point (11, 4).
  51. 4(c)5 marks· CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2A point, Q, moves in the x-y plane such that it is equidistant from A(2, -5) and B(-2, 3). Determine the locus of Q.
  52. 3(c)5 marks· CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2Determine the equation of the circle that has (1, 0) and (3, 2) as endpoints of a diameter.
  53. 3(d)8 marks· CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2Determine the points of intersection of the curves 2x² - y - 11 = 0 and x² - 4x - y + 10 = 0.
  54. 4(a)8 marks· CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2Determine the equation of the normal to the curve x = t², y = t + 1/t at the point on the curve where t = 2.
  55. 1(a)9 marks· Pure Mathematics · Unit 1 Q1 1(a)Find the coordinates of A and B.
  56. 1(a)8 marks· Pure Mathematics · Unit 1 Q1 1(a)Solve the simultaneous equations x² + xy = 6 and x - 3y + 1 = 0.
  57. 1(a)8 marks· Pure Mathematics · Unit 1 Q1 1(a)Solve the simultaneous equations: (x - 2)² + (y+2)² = 4, y+x-2=0.
  58. 1(b)(i)1 mark· Pure Mathematics · Unit 1 Q1 1(b)(i)Write down the size of angle PQR.
  59. 1(b)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(b)(ii)Calculate, in terms of r, the area of triangle PQR.
  60. 1(b)(iii)1 mark· Pure Mathematics · Unit 1 Q1 1(b)(iii)Write down the size of angle PSQ.
  61. 1(b)(iv)2 marks· Pure Mathematics · Unit 1 Q1 1(b)(iv)By considering triangle PSR, or otherwise, show that r/(r+α) = √3/2.
  62. 1(b)(v)6 marks· Pure Mathematics · Unit 1 Q1 1(b)(v)Calculate, in terms of r, the area of the shaded region.
  63. 2(c)(ii)2 marks· Pure Mathematics · Unit 1 Q2 2(c)(ii)Find an equation connecting x and y.
  64. 3(a)5 marks· Pure Mathematics · Unit 1 Q3 3(a)Express the equation of Q in the form (x - a)² + (y - b)² = c.
  65. 3(a)7 marks· Pure Mathematics · Unit 1 Q3 3(a)Find the coordinates of A, B and C.
  66. 3(a)(i)2 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)Determine the length of the radius of the circle.
  67. 3(a)(i)2 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)State the values of tan α and tan β.
  68. 3(a)(i)2 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)State the radius and the coordinates of the centre of C.
  69. 3(a)(i)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)Find the coordinates of the centre and radius of the circle x² + 2x + y² – 4y = 4.
  70. 3(a)(i)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)Find the equation of the line AB.
  71. 3(a)(i)3 marks· Pure Mathematics · Unit 1 Q3 3(a)(i)Find the equation of the line which passes through the point (4, -1) and is perpendicular to the straight line y = -2x + 2.
  72. 3(a)(ii)5 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)By writing x + 1 = 3 sin θ, show that the parametric equations of this circle are x = -1 + 3 sin θ, y = 2 + 3 cos θ.
  73. 3(a)(ii)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)Find the equation of the line PQ.
  74. 3(a)(ii)5 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)Show that the Cartesian equation of the tangent to the curve at the point P with parameter T is Ty = x + 4T².
  75. 3(a)(ii)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)Find the equation of the tangent at the point (6, 8) on C.
  76. 3(a)(ii)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)Without using tables or calculators, find the tangent of the angle between the two lines.
  77. 3(a)(ii)1 mark· Pure Mathematics · Unit 1 Q3 3(a)(ii)Determine the equation of the circle.
  78. 3(a)(ii)3 marks· Pure Mathematics · Unit 1 Q3 3(a)(ii)Calculate the coordinates of the point of intersection of these two straight lines.
  79. 3(a)(iii)6 marks· Pure Mathematics · Unit 1 Q3 3(a)(iii)Determine the coordinates of the points A and B, at which the circle cuts the x-axis.
  80. 3(a)(iii)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(iii)Show that the x-coordinates of the points of intersection of this circle with the line x + y = 1 are x = -1 + (3√2)/2.
  81. 3(a)(iii)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(iii)Find the coordinates of the point Q.
  82. 3(a)(iii)6 marks· Pure Mathematics · Unit 1 Q3 3(a)(iii)The tangent in (ii) above meets the y-axis at the point Q and the x-axis at the point R. If O is the origin, show that the area of triangle OQR is 8T³ square units.
  83. 3(a)(iii)7 marks· Pure Mathematics · Unit 1 Q3 3(a)(iii)Calculate the coordinates of the points of intersection of C with the straight line y = 2x + 3.
  84. 3(a)(iv)4 marks· Pure Mathematics · Unit 1 Q3 3(a)(iv)Determine the equation of the tangent at B.
  85. 3(a)(v)2 marks· Pure Mathematics · Unit 1 Q3 3(a)(v)Determine the coordinates of P.
  86. 3(b)7 marks· Pure Mathematics · Unit 1 Q3 3(b)Find the equations of the lines CD and AD.
  87. 3(b)5 marks· Pure Mathematics · Unit 1 Q3 3(b)Show by calculation that PD = PB.
  88. 3(b)(i)2 marks· Pure Mathematics · Unit 1 Q3 3(b)(i)Hence, or otherwise, state the coordinates of the centre of Q.
  89. 3(b)(i)2 marks· Pure Mathematics · Unit 1 Q3 3(b)(i)Show that L passes through the centre of C.
  90. 3(b)(i)6 marks· Pure Mathematics · Unit 1 Q3 3(b)(i)Show that the equation of C₁ is x² + y² + 2x – 6y + 5 = 0.
  91. 3(b)(i)4 marks· Pure Mathematics · Unit 1 Q3 3(b)(i)Find the cartesian equation of the curve, C.
  92. 3(b)(ii)1 mark· Pure Mathematics · Unit 1 Q3 3(b)(ii)Hence, or otherwise, state the radius of Q.
  93. 3(b)(ii)3 marks· Pure Mathematics · Unit 1 Q3 3(b)(ii)If L intersects C at P and Q, determine the coordinates of P and Q.
  94. 3(b)(ii)9 marks· Pure Mathematics · Unit 1 Q3 3(b)(ii)Calculate the coordinates of the points of intersection of C₁ and C₂.
  95. 3(b)(ii)3 marks· Pure Mathematics · Unit 1 Q3 3(b)(ii)Describe the curve, C, in detail.
  96. 3(b)(iii)3 marks· Pure Mathematics · Unit 1 Q3 3(b)(iii)Find the constants a, b and c such that x = b + a cos θ and y = c + a sin θ are parametric equations (in parameter θ) of C.
  97. 3(b)(iii)5 marks· Pure Mathematics · Unit 1 Q3 3(b)(iii)Find the equations of the tangent and normal to the curve, C, at the point given by θ = 0.
  98. 3(b)(iv)7 marks· Pure Mathematics · Unit 1 Q3 3(b)(iv)Another circle C₂, with the same radius as C, touches L at the centre of C. Find the possible equations of C₂.
  99. 3(c)5 marks· Pure Mathematics · Unit 1 Q3 3(c)Find the coordinates of the point D.
  100. 3(c)3 marks· Pure Mathematics · Unit 1 Q3 3(c)Show that the point A(4, 3) lies on Q.
  101. 3(d)6 marks· Pure Mathematics · Unit 1 Q3 3(d)Calculate the area of triangle ACD.
  102. 3(d)5 marks· Pure Mathematics · Unit 1 Q3 3(d)Find the equation of the tangent to Q at the point A.
  103. 3(e)4 marks· Pure Mathematics · Unit 1 Q3 3(e)The centre of Q is the midpoint of its diameter AB. Find the coordinates of B.
  104. 4(a)8 marks· Pure Mathematics · Unit 1 Q4 4(a)Calculate the distance between the points of intersection of the line 3x – 2y + 6 = 0 and the circle x² + y² = 9.
  105. 4(a)(i)4 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Determine the centre and radius of the circle.
  106. 4(a)(i)6 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)The line x - 2y + 4 = 0 cuts the circle, x² + y² - 2x - 20y + 51 = 0 with centre P, at the points A and B. Find the coordinates of P, A and B.
  107. 4(a)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Determine the centre and radius of the circle, C.
  108. 4(a)(i)4 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Determine the Cartesian equations of C₁ and C₂ in the form (x – a)² + (y – b)² = r².
  109. 4(a)(i)8 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Find the equation of the line which passes through M and is perpendicular to PQ.
  110. 4(a)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Show that the centre and the radius of the circle, C, are (3, 2) and 3, respectively.
  111. 4(a)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Show that the coordinates of the centre of the circle, C, where L₁ and L₂ intersect are (2, 3).
  112. 4(a)(i)5 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Determine the Cartesian equation of the curve, C, defined by the parametric equations y = 3 sec θ and x = 3 tan θ.
  113. 4(a)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Express the equation of C₂ in the form (x – h)² + (y - k)² = k.
  114. 4(a)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(i)Find the equation connecting x and y.
  115. 4(a)(ii)5 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Hence, or otherwise, determine the Cartesian equation of the curve defined parametrically by y = tan(2t) and x = sin(t) for 0 < t < π/2.
  116. 4(a)(ii)9 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Find the points of intersection of the curve y = √10x with C.
  117. 4(a)(ii)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)determine the coordinates of B.
  118. 4(a)(ii)9 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Hence, or otherwise, find the coordinates of the centre of the circle through P, O and Q.
  119. 4(a)(ii)6 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Show that (1, -2) is one of the points of intersection of the circle, C, and the straight line, L.
  120. 4(a)(ii)7 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)The equation of the line L₁ is x + 3y = 3. Determine whether L₁ is a tangent to the circle, C₁, in a (i) on page 16.
  121. 4(a)(ii)9 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Hence or otherwise, find the points of intersection of C₁ and C₂.
  122. 4(a)(ii)4 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Determine the equation of the tangent which touches the circle at (3, 11).
  123. 4(a)(ii)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)Show that the equation represents a circle, C.
  124. 4(a)(ii)a)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)a)Find the equation of the normal to the circle C at the point (6, 2).
  125. 4(a)(ii)b)2 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)b)Find the equation of circle C.
  126. 4(a)(ii)b)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)b)Show that the tangent to the circle at the point (6, 2) is parallel to the y-axis.
  127. 4(a)(ii)c)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)c)Find the distance, | PQ |, between the centres.
  128. 4(a)(ii)d)4 marks· Pure Mathematics · Unit 1 Q4 4(a)(ii)d)Find the distance | PM | if PQ cuts AB at M.
  129. 4(a)(iii)3 marks· Pure Mathematics · Unit 1 Q4 4(a)(iii)A point, p, moves in the x - y plane such that its distance from C (2, 3) is always √2 units. Determine the locus of p.
  130. 4(a)(iii)4 marks· Pure Mathematics · Unit 1 Q4 4(a)(iii)Determine the equation of the tangent to the circle, C, at the point (1, -2).
  131. 4(a)(iii)2 marks· Pure Mathematics · Unit 1 Q4 4(a)(iii)Determine the centre and radius of C.
  132. 4(b)5 marks· Pure Mathematics · Unit 1 Q4 4(b)Show that the curve whose parametric equations are x = 3 + 3 sin θ and y = 3 cos θ represents a circle.
  133. 4(b)12 marks· Pure Mathematics · Unit 1 Q4 4(b)Show that the equation of the locus of the point P (x, y) is a circle.
  134. 4(b)4 marks· Pure Mathematics · Unit 1 Q4 4(b)is 4x = y² + 10y + 24.
  135. 4(b)6 marks· Pure Mathematics · Unit 1 Q4 4(b)Determine the Cartesian equation of the curve, S.
  136. 4(b)(i)5 marks· Pure Mathematics · Unit 1 Q4 4(b)(i)Find the centre and radius of C.
  137. 4(b)(i)6 marks· Pure Mathematics · Unit 1 Q4 4(b)(i)Prove that the line y = x + 1 is a tangent to the circle x² + y² + 10x – 12y + 11 = 0.
  138. 4(b)(i)3 marks· Pure Mathematics · Unit 1 Q4 4(b)(i)Show that the Cartesian equation of the curve is (x-2)²/9 + (y-3)²/16 = 1.
  139. 4(b)(ii)3 marks· Pure Mathematics · Unit 1 Q4 4(b)(ii)Show that the equation in (i) represents a circle, C.
  140. 4(b)(ii)4 marks· Pure Mathematics · Unit 1 Q4 4(b)(ii)Find the equation of the tangent to C at the point (0,0).
  141. 4(b)(ii)2 marks· Pure Mathematics · Unit 1 Q4 4(b)(ii)Find the coordinates of the point of contact of this tangent to the circle.
  142. 4(b)(ii)5 marks· Pure Mathematics · Unit 1 Q4 4(b)(ii)Show that every point on the curve lies within or on the circle (x – 2)² + (y - 3)² = 25.
  143. 4(b)(iii)4 marks· Pure Mathematics · Unit 1 Q4 4(b)(iii)Determine the centre and radius of the circle C.
  144. 4(c)5 marks· Pure Mathematics · Unit 1 Q4 4(c)Determine the Cartesian equation of the locus of P.
  145. 4(d)5 marks· Pure Mathematics · Unit 1 Q4 4(d)Determine the points of intersection of the circle C and the line L.
  146. 5(b)(ii)3 marks· Pure Mathematics · Unit 1 Q5 5(b)(ii)Determine the value of t for which the circle has vertical tangents.
  147. 5(b)(ii)5 marks· Pure Mathematics · Unit 1 Q5 5(b)(ii)the equation of the tangent to the curve at the point where x = 1/2.
  148. 5(c)(i)3 marks· Pure Mathematics · Unit 1 Q5 5(c)(i)Find the coordinates of P.
  149. 5(c)(iii)2 marks· Pure Mathematics · Unit 1 Q5 5(c)(iii)Find the length of MN.
  150. 5(d)(i)4 marks· Pure Mathematics · Unit 1 Q5 5(d)(i)Determine the coordinates of the points P and Q at which the curve and the line intersect.
  151. 6(a)(i)1 mark· Pure Mathematics · Unit 1 Q6 6(a)(i)On the axes below, sketch triangle PQR.
  152. 6(a)(i)5 marks· Pure Mathematics · Unit 1 Q6 6(a)(i)Show that the coordinates of A, B and C are (4, 5), (3, 2), and (6, 3) respectively.
  153. 6(a)(ii)7 marks· Pure Mathematics · Unit 1 Q6 6(a)(ii)Determine the equations of EACH of the following: PQ, QR, PR.
  154. 6(b)(i)2 marks· Pure Mathematics · Unit 1 Q6 6(b)(i)Show that r = (600-2x) / (2 + π)
  155. 6(b)(i)4 marks· Pure Mathematics · Unit 1 Q6 6(b)(i)Find the equation of C.
  156. 6(b)(ii)8 marks· Pure Mathematics · Unit 1 Q6 6(b)(ii)Determine the equation of the normal to the curve at the point (√3, 5/2).
  157. 6(b)(iv)5 marks· Pure Mathematics · Unit 1 Q6 6(b)(iv)Find the coordinates of the points P and Q at which the curve C meets the x-axis.
  158. 6(c)(i)6 marks· Pure Mathematics · Unit 1 Q6 6(c)(i)Find the coordinates of A, B and C.
  159. 6(c)(i)5 marks· Pure Mathematics · Unit 1 Q6 6(c)(i)Find the coordinates of the points P and Q.

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