# Homework help

1. Jul 17, 2004

Got a problem which should be easy but having trouble...

"Find the equation of the tangent plane to z=f(x,y)=x^2 + y^2 - 1 at point (1,1,1)
"Find an equation to a plane that is perpendicular to that tangent plane and also passes through the point (1,1,1)

Thanks!

2. Jul 17, 2004

### arildno

Welcome to PF!

Are you familiar with the theorem that the gradient of a surface G(x,y,z)=0 is normal to that surface?
Use that hint (G(x,y,z)=z-f(x,y)).

3. Jul 17, 2004

I figured out the first part of the problem the tangent plane to f(x,y) is 2x+2y-z-3=0. The normal vector of that plane is thus <2,2,-1>. I am lost on how to solve the next part, I keep trying different equations but coming up with too many variables.

4. Jul 17, 2004

### arildno

There's an infinity of planes which are normal to the tangent plane.
Pick one of them; the requirement is merely that some tangent vector in the tangent plane should be the normal to the plane you choose.
(the normal of the tangent plane is to be a tangent vector in the plane you choose)

Last edited: Jul 17, 2004
5. Jul 17, 2004

### Gokul43201

Staff Emeritus
"too many variables" only allows you to set one of them to any convenient value. Like arildno said, there are an infinite number of normal planes passing through a given point; so you get to pick any one you like.