Tangent plane confusion

1. Feb 19, 2015

Calpalned

1. The problem statement, all variables and given/known data
What's the difference between the two equations for a plane?

This question is somewhat related to my other, overarching question here: https://www.physicsforums.com/threads/i-am-confused-about-how-multivariable-calc-works.798798/

2. Relevant equations
$a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$
and
$z - z_0 = f_x (x_0, y_0)(x-x_0) + f_y (x_0, y_0)(y-y_0)$

3. The attempt at a solution
I'm not sure what the relationship between these two equations are. Thanks everyone.

Last edited: Feb 19, 2015
2. Feb 19, 2015

Dick

There's no deep difference. The first is the general form of a plane with $(a,b,c)$ as a normal vector. The second is a specific example of a plane corresponding to a tangent surface with normal vector $(f_x,f_y,-1)$.