# Thread: tangent plane to the surface

1. ## tangent plane to the surface

find the eqn of the tangent plane to the surface
z=f(x,y)=x^2 +4y^2

at the point (a,b,a^2 +4y^2)

What I don't understand is how the normal to the plane at point a,b is geven by:
n=(fx,fy,-1)

would fx not be the "rate of change with respect to x" and not the NORMAL to the plane at that point?

2. Consider the field $F(x,y,z) = x^2 + 4y^2 - z$. The surface we have is $F(x,y,z)=0$.
The normal at any point is $\nabla F(x,y,z) = \left\langle {F_x ,F_y ,F_z } \right\rangle$.
In this case it is $\left\langle {2x,8y, - 1} \right\rangle$ .

4. The expression $\nabla F(x,y,z) = \left\langle {F_x ,F_y ,F_z } \right\rangle$ is called the gradient of the field.
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