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M4U-9709-CG26-E-CI018 marks

E-CI01 · A circle and a tangent intercept

The circle \(x^2+y^2+2x-8y-8=0\) passes through \(P=(2,8)\).

Find its centre and radius, and verify that P is on the circle.

[3]

Find the tangent at P.

[2]

The tangent meets the x-axis at Q. Find Q and the exact length PQ.

[3]
A circle with one labelled pointCircle x²+y²+2x−8y−8=0 with P(2,8) marked on the circumference; centre not marked.P(2,8)
The equation, rather than the drawing, determines the centre and radius.

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