Find an equation for the tangent plane to the surface x^2+y^2-z=0 at the point (1,1,2).

Your solution will be of the form , where are constants.

Note that are simply the coordinates of . So, your solution will look something like this:

.

We want to find the constants a, b, and c. How? We first compute the partial derivatives of our surface equation .

The gradient vector is given by:

.

So, .

Then, plugging in the coordinates of , we get:

So0oo, the constants , respectively.

Soooooooo, the equation for the tangent plane to the surface is

.

Rearrange this if you so wish.

Enjoy,

-Andy