Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

For the circle with centre $C$, the equation is $x^2 + y^2 - 8x + 4y - 5 = 0$.
(a)[3]

Find the radius of the circle and the coordinates of $C$.

(b)[3]

Point $P\,(1, 2)$ lies on the circle. Show that the equation of the tangent to the circle at $P$ is $4y = 3x + 5$.

(c)[2]

The point $Q$ also lies on the circle and $PQ$ is parallel to the $x$-axis. Write down the coordinates of $Q$.

(d)[3]

The tangents drawn at $P$ and $Q$ meet at $T$. Find the coordinates of $T$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Complete the square to get $(x-4)^2+(y+2)^2=25$

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