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WAEC Further Mathematics 2011 Question 22

Question 22

Coordinate Geometry

Find the equation of a circle with centre (−3, −8) and radius 4√6.

  1. A.x2 − y2 − 6x + 16y + 23 = 0
  2. B.x2 + y2 + 6x + 16y − 23 = 0
  3. C.x2 + y2 + 6x − 16y + 23 = 0
  4. D.x2 + y2 + 6x + 16y + 23 = 0
Show the answer and explanation

Answer: B (x2 + y2 + 6x + 16y − 23 = 0)

Explanation

(x + 3)2 + (y + 8)2 = 96. Expanding: x2 + y2 + 6x + 16y + 73 − 96 = 0, i.e. x2 + y2 + 6x + 16y − 23 = 0.