Maximum distance of point from curve

Question

Prove that the maximum distance of the point $(k,0) $ from the curve $2x^2+y^2-2x=0$ is $\sqrt{1-2k+2k^2}$.

I know that minimum distance is achieved along the normal to the curve from that point. Could someone give me hint to find maximum distance?

Answer 1

Hint: maximize the function $$f(x)=\sqrt{(x-k)^2+2x-2x^2}$$ with respect to $x$