Mathematics 0580 · IGCSE · Coordinates

Coordinates — practice question

The diagram depicts a curve whose equation is $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$.
(a(i))[3]

Find the equation of the straight line through $A$ and $B$. Give your answer in the form $y=mx+c$.

(a(ii))[2]

Show that $a^2=16$ and $b^2=4$.

(b(i))[3]

Find the value of $k$.

(b(ii))[3]

Calculate angle $POQ$.

(c(i))[1]

Find the area enclosed by the curve $\dfrac{x^2}{16}+\dfrac{y^2}{4}=1$. Give your answer as a multiple of $\pi$.

(c(ii))[2]

Work out the area enclosed by this curve, giving your answer as a multiple of $\pi$.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: Gradient $-\frac{1}{2}$

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