Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

A circle is given by $(x - 6)^2 + (y + a)^2 = 18$. The line $y = 2a - x$ touches the circle, so it is a tangent.

(a)[5]

Determine the two possible values of $a$.

(b)[3]

For the larger value of $a$, determine the equation of the diameter that is perpendicular to the stated tangent.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replaces $y=2a-x$ in the circle equation” …