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 $-2$

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