2025 PHS P1 Q13

2025 PHS P1 Q13

Secondary 4
6 marks

The equation of a circle is \(x^2-4x+y^2-6y+c=0\), where \(c\) is a constant to be determined.

  1. Find the coordinates of the centre of the circle.[2]
  2. Given that \(y=7\) is a tangent to the circle, show that the value of \(c\) is \(-3\).[2]
  3. The equation of a normal to the circle is \(2y+x=k\). Find the value of \(k\).[2]

Solution:

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Answer:(a) \((2,3)\). (b) \(c=-3\) (shown). (c) \(k=8\).

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