Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram displays circle $P$, whose centre is $(0, 2)$ and whose radius is $10$, together with the tangent to the circle at $A(6, 10)$. It also displays a second circle $Q$, centred at the point where this tangent crosses the $y$-axis, with radius $\frac{5}{2}\sqrt{5}$.
(a)[1]
State the equation of circle $P$.
(b)[2]
Find the equation for the tangent to circle $P$ at $A$.
(c)[3]
Find the equation of circle $Q$ and hence confirm that the $y$-coordinates of both intersection points of the two circles are $11$.
(d)[3]
Find the coordinates of the intersection points of the tangent and circle $Q$, giving your answers in surd form.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct equation of circle: $x^2+(y-2)^2=100$” …