Finding parametric equations of a tangent line

1. Dec 13, 2008

grog

1. The problem statement, all variables and given/known data

Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4

2. Relevant equations

Not sure

3. The attempt at a solution

Not sure quite how to approach this. take the gradient of 2x^2-y^2 and just plug for x=rcos$$\Theta$$ and y=r sin$$\Theta$$ ?

That seems too simple..

2. Dec 13, 2008

Dick

The gradient gives you a normal direction for each surface. Then the tangent is perpendicular to both normals. How can you find a vector perpendicular to two other vectors?

3. Dec 13, 2008

grog

so I would end up with 4x-2y and zero for the two normal vectors? and then take the cross product of the two? I think I may be confusing some concepts here.

4. Dec 13, 2008

Dick

Probably. The gradient is a vector. Those don't look like vectors. Better check the definition of 'gradient'.