A curve $C$ has equation $y=\frac{1}{\sqrt{4ax-{{x}^{2}}}}$, where $a 0$. Sketch \(C

Question

A curve $C$ has equation $y=\frac{1}{\sqrt{4ax-{{x}^{2}}}}$, where $a > 0$. Sketch $C$ and give the equations of any asymptotes, in terms of $a$ where appropriate.[4] Find the smallest possible value of $y$ in terms of $a$.[1] Describe the transformation that maps the graph of $C$ onto the graph of $y=\frac{1}{\sqrt{4{{a}^{2}}-{{x}^{2}}}}$.[3]

Accepted Answer

(a) Graph with VA at $x = 0$ and $x = 4a$, min at $(2a, \frac{1}{2a})$ (b) $\frac{1}{2a}$ (c) Translation of $2a$ units in negative $x$ direction

N2021 P1 Q6

N2021 P1 Q6

Video Solution:

Default solution