$\text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is }$

The curve $x^2 = xy$ can be rewritten as $x(x-y) = 0$, giving two lines: $x = 0$ (y-axis) and $y = x$.

Checking if $(0,5)$ lies on the curve: substituting $x = 0$ gives $0 = 0$, which is satisfied.

So $(0,5)$ already lies on the curve (on the $x = 0$ branch), and the distance is exactly 0.

The closest point is $(0, 5)$ itself.