# The formula for a tangent plane to a surface

1. Aug 24, 2009

### Mazzur

Hey I'm trying to understand how we arrive at the formula for the tangent plane to a surface. An image of what i'm talking about it shown below.

I think understand all the parts up to part c, but i don't see how we arrive at that final formula. The image of first part of the solution is shown just to provide context.

2. Aug 30, 2009

### tiny-tim

Welcome to PF!

Hey Mazzur! Welcome to PF!

∂f/dx|ro ∂f/dy|ro and ∂f/dz|ro are all constants, and they are the constants that have to be the coefficients of x y and z …

that's the bit you understand, isn't it?

So the equation has to be
∂f/dx|rox + ∂f/dy|ro y + ∂f/dz|roz = constant,

and all they've done is to put that constant on the left of the = sign, and split it up between the three coordinates.

If you prefer, you can put it back on the right, like this …

∂f/dx|rox + ∂f/dy|ro y + ∂f/dz|roz = ∂f/dx|roxo + ∂f/dy|ro yo + ∂f/dz|rozo

either way, you can see that putting x = xo, y = yo, z = zo, makes the equation true.