2025 IGCSE Additional Mathematics May/June 0606/12 Q3

2025 IGCSE Additional Mathematics May/June 0606/12 Q3

8 marks

A circle with centre \(C\) has the equation \(x^2+y^2-10x-4y+24=0\).

  1. Show that the line \(y=2x-3\) is a tangent to this circle.[3]
  2. Given that this tangent touches the circle at the point \(P\), find the coordinates of \(P\).[2]
  3. Find the equation of the circle which has its centre at \(P\) and passes through the origin.[3]

Solution:

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Answer:(a) \(5(x-3)^2=0\) gives tangency (shown) (b) \(P=(3,3)\) (c) \((x-3)^2+(y-3)^2=18\)

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