8 A curve \(C\) has equation \(x ^ { 2 } + 4 x y - y ^ { 2 } + 20 = 0\). Show that, at stationary points on \(C , x = - 2 y\).
Find the coordinates of the stationary points on \(C\), and determine their nature by considering the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the stationary points.
8 A curve $C$ has equation $x ^ { 2 } + 4 x y - y ^ { 2 } + 20 = 0$. Show that, at stationary points on $C , x = - 2 y$.
Find the coordinates of the stationary points on $C$, and determine their nature by considering the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ at the stationary points.
\hfill \mbox{\textit{CAIE FP1 2016 Q8}}