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5 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 2 · Question 3(a)

The equation of the circle, Q, with centre O is x² + y² - 2x + 2y = 23.

Express the equation of Q in the form (x - a)² + (y - b)² = c.

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Other parts of this question

  1. 3(b)(i)Hence, or otherwise, state the coordinates of the centre of Q.[2 marks]
  2. 3(b)(ii)Hence, or otherwise, state the radius of Q.[1 mark]
  3. 3(c)Show that the point A(4, 3) lies on Q.[3 marks]
  4. 3(d)Find the equation of the tangent to Q at the point A.[5 marks]
  5. 3(e)The centre of Q is the midpoint of its diameter AB. Find the coordinates of B.[4 marks]

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