Use Lagrange multipliers to find the point on the curve 5x^2 - 6xy + 5y^2 = 64 which is closets to the origin.

Use Lagrange multipliers to find the point on the curve 5x^2 - 6xy + 5y^2 = 64 which is closets to the origin.

1) DelF = Landa*DelG

2) origin (0,0,0)

I'm confused on the distance formula aspect of this problem. Is the given equation (5x^2 - 6xy + 5y^2 = 64) the constraint? and how do I use the distance formula D^2 = x^2 +y^2 +z^2 to help apply to this problem? Also can you help me visualize the problem with the level curve aspect of it?