I was given the question:
Consider the point $P = (3, 4, 0)$ and the cone $z^2 = x^2 + y^2$. Determine the point on the cone that minimizes the square of the distance between $P$ and the cone.
Am I supposed to be minimizing the distance formula between point $P$ and the equation of the cone?
It is $$f(x,y)=(x-3)^2+(y-4)^2+x^2+y^2$$ It is $$f(x,y)\geq \frac{25}{2}$$ and the equal sign holds if $$x=\frac{3}{2},y=2$$