Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The circle has centre $C(-4, 5)$ and radius $\sqrt{20}$ units, as shown in the diagram. It meets the $y$-axis at $A$ and $B$. The angle $ACB$ has size $\theta$ radians.
(a)[3]
Calculate the equation of the tangent to the circle at the point $(-6, 9)$.
(b)[2]
Determine the equation of the circle in the form $x^2 + y^2 + ax + by + c = 0$.
(c)[3]
Determine the value of $\theta$ correct to 4 significant figures.
(d)[4]
Calculate the perimeter and area of the shaded segment in the diagram.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The gradient of the relevant radius is $-2$” …