2025 CGS PRELIMS P2 Q7

2025 CGS PRELIMS P2 Q7

Secondary 4
7 marks
2025 Crescent Girls' School Prelims A Math Paper 2

The equation of a circle with centre \(C\) is \(x^2 + y^2 - 8x - 10y + 16 = 0\).

A point \(B\,(7, 9)\) lies on the circumference of the circle. \(P\) is the lowest point on the circle.

  1. Find the coordinates of \(C\) and the radius of the circle.[3]
  2. Find the equation of the tangent to the circle at \(B\).[3]
  3. Explain why \(P\) lies on the \(x\)-axis.[1]

Solution:

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Answer:(a) \(C=(4,5),\ r=5\) (b) \(3x+4y=57\) (c) \(y_P=0\), so \(P\) lies on the \(x\)-axis.

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