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WAEC Further Mathematics 2018 Question 23

Question 23

Coordinate Geometry

Find the equation of the tangent to the circle x2 + y2 − 4x − 2y = 0 at the point (1, 3)

  1. A.2y − x − 5 = 0
  2. B.2y + x − 5 = 0
  3. C.2y + x + 5 = 0
  4. D.2y − x + 5 = 0
Show the answer and explanation

Answer: A (2y − x − 5 = 0)

Explanation

Centre (2, 1). The radius to (1, 3) has gradient −2, so the tangent has gradient ½: y − 3 = ½(x − 1), i.e. 2y − x − 5 = 0.