3 The function f is defined by \(\mathrm { f } ( x ) = \frac { 5 a x } { x ^ { 2 } + a ^ { 2 } }\), for \(x \in \mathbb { R }\) and \(a > 0\).
- For the curve with equation \(y = \mathrm { f } ( x )\),
(a) write down the equation of the asymptote,
(b) find the range of values that \(y\) can take. - For the curve with equation \(y ^ { 2 } = \mathrm { f } ( x )\), write down
(a) the equation of the line of symmetry,
(b) the maximum and minimum values of \(y\),
(c) the set of values of \(x\) for which the curve is defined.