Math Is Fun Forum

dexza666

Member

Registered: 2008-04-21

Posts: 5

tangent planes

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).

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: tangent planes

I tried to learn from luca, and of course the (1,2,3) is not
right if you just plug them in, the z's don't match.
So I set f(x,y,z) = 0 like luca,
and did partial deriv's.
Then set the df/dx ones equal to each other to see
what would happen, and I got
-145 = 34x^2 + 34y^2, which can't happen.
Don't know what this means.
Thanks to luca though for these amazing posts!!
I'm learning a lot!

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igloo myrtilles fourmis

dexza666

Member

Registered: 2008-04-21

Posts: 5

Re: tangent planes

Differentiate....then evaluate both at 1,2,3 see if that helps

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: tangent planes

The df/dz is always -1, just a constant I think.
So the df/dx 's are different anyway:  1/9 and 2/3   at (1,2) for (x,y) and the z is not part of their slope equations.

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igloo myrtilles fourmis

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: tangent planes

plugging in x=1,y=2

now the problem here though, is that although x_1,y_1 is related to x_2,y_2 by a multiple of 6, this is not the case for z_1 and z_2 so really, they are not colinear vectors, and the surfaces are not tangentenial?

either i did something wrong, or the question/answer is incorrect

Last edited by luca-deltodesco (2008-04-23 03:08:47)

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