9758/2021/P1/Q06

A curve $C$ has equation $y=\frac{1}{\sqrt{4 a x-x^2}}$, where $a>0$.
(a) Sketch $C$ and give the equations of any asymptotes, in terms of $a$ where appropriate.

[4]

(b) Find the smallest possible value of $y$ in terms of $a$.

[1]

(c) Describe the transformation that maps the graph of $C$ onto the graph of $y=\frac{1}{\sqrt{4 a^2-x^2}}$.

[3]