Euclidian projection on ellipsoid and conic

Find the projection of point P in R^n on the ellipsoidE = { x = x0 + U*(z.*radii) : |z| = 1 }, where U is orthogonal matrix of the orientation of E, radii are the axis lengths, and x0 is the center.Or on generalized conic E = { x : x'*A*x + b'*x +...