# Thread: CALC III ELLIPTIC PARABOLLOID need it completely solved

1. ## CALC III ELLIPTIC PARABOLLOID need it completely solved

Find all points on the elliptic paraboloid at which the normal line to the tangent plane coincides with the line joining the origin to the point (or, equivalently the normal vector to the tangent plane is parallel to the vector from the origin to the point).

this was slightly solved, but when you get to the system of equations to find points... i have no idea what to do to solve this problem

2. In other word, you search the point that is closest to the origin. The function of distance from the origin is
$d^2=x^2+y^2+z^2$ you want to optimize this function with the constraint $z= x^2+2y^2-1$
Use Lagrange multipliers.
You will get two answers.
You will get $(0,\pm\sqrt{\frac{3}{8}},-\frac{1}{4})$