2025 Paradigm Sec 3 Mock EOY Q13

2025 Paradigm Sec 3 Mock EOY Q13

Secondary 3
9 marks

[Circles]

A circle, centre \(C\), has a chord \(AB\), where \(A\) is the point \((7,27)\) and \(B\) is the point \((-11,15)\). The normal at \(A\) passes through the point \(D(-3,3)\).

  1. Showing all your working, find the equation of the circle.[7]
  2. Show that \(D\) lies on the circle.[2]

Solution:

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Answer:(a) \((x-2)^2+(y-15)^2=169\); (b) \(D(-3,3)\) satisfies the equation.

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