2023 KSS P2 Q6

2023 KSS P2 Q6

Secondary 4
11 marks

The equation of a circle is \(x^2+y^2-4x+6y-12=0\).

  1. Find the radius and the coordinates of the centre, \(C\), of the circle.[3]

The point \(P(5,1)\) lies on the circle.

  1. Find the equation of the tangent to the circle at \(P\).[4]
  2. The tangent at \(P\) intersects the axes at \(A\) and \(B\). Find the area of the triangle \(ABC\).[4]

Solution:

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Answer:(i) Radius 5; \(C=(2,-3)\). (ii) \(y=-\dfrac34x+\dfrac{19}4\). (iii) \(\dfrac{475}{24}\text{ units}^2\).

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