Tangent Planes: Proof of Tangential Surfaces at (1,2,3) with Differentiation

[dexza666]

Two surfaces are said to be tangential at a point P if they have the same
tangent plane at P . Show that the surfaces z = √(2x²+2y²-1) and z = (1/3)√(x²+y²+4) are tangential at the point (1, 2, 3).

differentiate first then evaluate both at 1,2,3

 

[HallsofIvy]

First, I find it hard to believe this is not schoolwork and I am going to move it to the homework section.

Secondly you should understand that you must show some work and not just expect someone to tell you how to do it.

In fact, it looks like you have been told how to do it: "differentiate first then evaluate both at 1,2,3". Have you done that?

I must say that I foresee a serious problem in "showing that the surfaces are tangential at (1, 2, 3)"! You might try first evaluating the second one at x= 1, y= 2. What do you get for z?