2026 CSS P2 Q7

2026 CSS P2 Q7

Secondary 4
10 marks

A circle, \(C_1\), has a diameter \(AB\) where \(A\) is the point \((12,-4)\) and \(B\) is the point \((24,12)\).

  1. Find the coordinates of the centre and the radius of \(C_1\).[2]
  2. Find the equation of \(C_1\) in the form \(x^2+y^2+Ax+By+C=0\).[1]
  3. Find the equation of the tangent at \(A\).[4]

A second circle, \(C_2\), has equation \((x-6)^2+(y+1)^2=9\).

  1. Explain if the circles \(C_1\) and \(C_2\) intersect at two points, one point or does not intersect each other.[3]

Solution:

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Answer:(a) Centre \((18,4)\), radius 10. (b) \(x^2+y^2-36x-8y+240=0\). (c) \(y=-\dfrac34x+5\). (d) One point, external tangency.

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