How to Put Gradient Vector into Implicit Form?

[Loppyfoot]

Homework Statement

Let f(x,y) = 5y^(2)-(2x^(2)+xy)

Then an implicit equation for the tangent plane to the graph of f at the point (0,-2) is

Homework Equations

The Attempt at a Solution

I understand that I should take the derivative to find the gradient vector. For the derivative, I get <-4x-y,10y-x>.

I plug in (O,-2) and get <2,-20>.

My question is, what should I do to put this into implicit form??

Thanks!

 

[LCKurtz]

$$z_{tp}(x,y) = f(x_0,y_0) + f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)$$