15 The curve with equation
$$x ^ { 2 } + 2 y ^ { 3 } - 4 x y = 0$$
has a single stationary point at \(P\) as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{6a03a035-ff32-4734-864b-a076aa9cbec0-26_656_1138_548_450}
15
- Show that the \(y\)-coordinate of \(P\) satisfies the equation
$$y ^ { 2 } ( y - 2 ) = 0$$
15
- Hence, find the coordinates of \(P\)
[0pt]
[2 marks]