Question

Find an equation of the plane trangent to the hyperboloid \[2x^2-3y^2+z^2=7\] at the point (3,2,1).

Answer 1

try visiting this url it might be able to explain this concept better than i can: http://math.etsu.edu/multicalc/archives/Chap3/Chap3-6/index.htm

Answer 2

did that help?

Answer 3

First you need to find the unit vector. You know how to find it?

Answer 4

yeah, I think I figured it out. Grad F(x,y,x)

Answer 5

so would it be. \[6(x-3) -6(y - 2) +(z-1) =0\] ?

Answer 6

You are right that's the equation for a plane passing through that point

Answer 7

yes

Answer 8

Sames right 6x-6y+z=9

Answer 9

actually that doesnt look right

Answer 10

The 9 should be 7

Answer 11

i got the same thing as lockdown but maybe i am wrong, i do know that you should most likely condense your answer

Answer 12

yeah, I condensed it. I got 12x - 12y + 2z - 14 = 0 originally, but divided by 2

Answer 13

Actually yeah

Answer 14

meaning combine constants on the other side of the equation

Answer 15

Here is a neat trick, Lockdown, rather than writing out the equation formula. Once you get your vector <6, -6, 1> Write it as an eq 6x-6y+1= The other side can be determined in your head by the points (6*3=18) -12 + 1=7

Answer 16

you know that trick is actually helpful to me too, thanks chaguanas

Answer 17

Yeah, the equation is taught in schools, mathematicians don't do it the eq way

Answer 18

yeah, thats a good way of thinking about it, since they always want simplified anyways.