2026 AHS P2 Q5

2026 AHS P2 Q5

Secondary 4
9 marks

The point \(P(-4,6)\) and \(Q(-7,3)\) lie on the circumference of a circle, \(C\), with centre \((a,b)\) and radius \(r\) units. The centre of the circle lies on the line \(y=4x+34\).

  1. Find the equation of the circle.[7]
  2. The point \(H(k,7)\) lies inside the circle. Find the set of possible values of \(k\).[2]

Solution:

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Answer:(a) \((x+7)^2+(y-6)^2=9\). (b) \(-7-2\sqrt2<k<-7+2\sqrt2\).

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