2026 GESS P1 Q6

2026 GESS P1 Q6

Secondary 4
12 marks

The equation of a circle \(C_1\), with centre \(A\), is \(x^2+y^2-4x+6y=12\).

  1. Find the coordinates of \(A\) and the radius of \(C_1\).[4]
  2. Show that the point \(P(6,0)\) lies on \(C_1\).[1]
  3. Find the equation of the tangent to \(C_1\) at \(P\).[3]

A second circle \(C_2\), has diameter \(AP\).

  1. Find the equation of \(C_2\).[3]
  2. State the equation of the tangent to \(C_2\) at \(P\).[1]

Solution:

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Answer:(a) \((2,-3)\), radius 5. (b) Shown. (c) \(y=-\dfrac43x+8\). (d) \((x-4)^2+(y+\dfrac32)^2=\dfrac{25}4\). (e) \(y=-\dfrac43x+8\).

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