3．The curve \(C\) has equation $$x ^ { 2 } + y ^ { 2 } + f x y = g ^ { 2 }$$ where \(f\) and \(g\) are constants and \(g \neq 0\) ．
（a）Find an expression in terms of \(\alpha , \beta\) and \(f\) for the gradient of \(C\) at the point \(( \alpha , \beta )\) ． Given that \(f < 2\) and \(f \neq - 2\) and that the gradient of \(C\) at the point \(( \alpha , \beta )\) is 1 ，
（b）show that \(\alpha = - \beta = \frac { \pm g } { \sqrt { } ( 2 - f ) }\) ． Given that \(f = - 2\) ，
（c）sketch \(C\) ．