# Homework Help: Intersection between surfaces

1. Jan 28, 2007

### bodensee9

1. The problem statement, all variables and given/known data
Hi, I need help with the following. I'm asked to find the parametric equation of the tangent line to the curve of the interrsection of the paraboloid z = x^2 + y^2 and the ellipsoid 4x^2+y^2+z^2 = 9 at the point (-1,1,2).

2. Relevant equations
I think I'm asked to find the gradient of the curves of the intersection, and then I know the vector with the direction of the line eof intersection, and then I can plug it back in to find the parametric equation of the line.

3. The attempt at a solution
I guess I am trying to find the equation of the curve of intersection first? So, would I set the two equations equal so that I would get 4x^2+y^2+(x^2+y^2)^2 = 9? But then z has gone away? I guess I'm pretty clueless as to how to attempt to solve this problem?
Or if I'm right that the intersection is an ellipse, but how am I supposed to find the equation of the ellipse? Can anyone give me any pointers or hints?

2. Jan 28, 2007

### AlephZero

You are only asked to find the tangent line at one particular point, so you don't need to find the equation of the complete intersection curve and then find its tangent. Doing all that would give you the answer, though.

Think about the tangent planes to the two surfaces at the point (-1,1,2).

3. Jan 28, 2007

### bodensee9

Was going to post. Figured it out. You only need to take the cross product of the gradient to the two curves.