Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

A circle centred at $C$ has equation $(x - 8)^2 + (y - 4)^2 = 100$.
(a)[3]

Show that the point $T(-6, 6)$ lies outside the circle.

(b)[2]

Two tangents are drawn from $T$ to the circle. Show that the angle between one of the tangents and $CT$ is $45^\circ$.

(c)[4]

The two tangents touch the circle at $A$ and $B$. Find the equation of line $AB$, giving your answer in the form $y = mx + c$.

(d)[3]

Find the $x$-coordinates of $A$ and $B$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The squared distance is $200$.

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