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WAEC Further Mathematics 2020 Question 24

Question 24

Coordinate Geometry

A circle with centre (5, −4) passes through the point (5, 0). Find its equation.

  1. A.x2 + y2 + 10x + 8y + 25 = 0
  2. B.x2 + y2 + 10x − 8y − 25 = 0
  3. C.x2 + y2 − 10x + 8y + 25 = 0
  4. D.x2 + y2 − 10x − 8y − 25 = 0
Show the answer and explanation

Answer: C (x2 + y2 − 10x + 8y + 25 = 0)

Explanation

The radius is the distance from (5, −4) to (5, 0) = 4. (x − 5)² + (y + 4)² = 16 gives x² + y² − 10x + 8y + 25 = 0.