CJC/2021/JC1/Promo/P1/Q10

The curves $C_1$ and $C_2$ have equations $y=\frac{2 x^2+9}{x^2-4}$ and $\frac{x^2}{9}+\frac{y^2}{25}=1$ respectively.
(i) Find the equations of the asymptotes of the curve $C_1$.

[3]

(ii) Sketch $C_1$ and $C_2$ on the same diagram, stating the equations of any asymptotes, coordinates of any points where $C_1$ or $C_2$ crosses the axes and any turning points.

[5]

(iii) Find the $x$-coordinates of the points where the two curves intersect.

[2]

(iv) Hence solve the inequality $-5 \sqrt{1-\frac{1}{9} x^2} \leq \frac{2 x^2+9}{x^2-4}$.

[2]