# hyperplane equation

• November 19th 2012, 04:12 PM
frankitm
hyperplane equation
Hi guys, i need some hints to solve this very difficult problem from vector calculus:
Attachment 25814

• November 23rd 2012, 10:00 AM
HallsofIvy
Re: hyperplane equation
The problem is to find the equation of the hyperplane tangent to the ellipse $x_1^2+ 2x_2^2+ 3x_3^2+ \cdot\cdot\cdot+ nx_n^2= \frac{n(n+1)}{2}$ at the point $(-1, -1, -1, \cdot\cdot\cdot, -1)$.

Now, what is your difficulty? Can you find the gradient of the function? That will give a vector perpendicular to the ellipse at the give point. Do you know how to write the equation of a hyperplane given a normal vector and point?