# Math Help - Tangent Line of Elliptic Paraboloid

1. ## Tangent Line of Elliptic Paraboloid

Hi, thank you in advance for responses.

For the elliptic paraboloid $z=4x^2+3y^2$, find a parametric equation of the tangent line to the paraboloid at the point (-1,2,16) in the x=-1 trace.

I've got a rough idea of how to do it, but I can't quite get there. You don't need to completely solve it for me if you don't want to, but some pointers in the right direction would be wonderful.

Thanks!

2. bump.

Okay, well I've been looking at it and I think that the line I'm trying to find is equal to the point + t * a vector.

Something like:

$r(t) = <-1,2,16>+t*$

Where r(t) is the line I'm trying to find.

Unfortunately, I do not know what that vector is or how to find it. Any ideas?