Question

Find equations of (a) th tangent plane and (b) the normal line to the given surface at the specific point.

A) 2(x-2)^2+(y-1)^2+(z-3)^2=10, P=(3,3,5)

Answer 1

I can get the answer, but it may take a bit.

Answer 2

yeh great, take your time...

Answer 3

I'll be back

Answer 4

Somebody may give the solution before I get back. If that happens, that's cool too.

Answer 5

ok I hope so, I really want to understand this

Answer 6

I think I got it! This is the solution for whoever would like to learn more about this topic:

First, we find the gradient of the Surface:
which is, del S = <4(x-2), 2(y-1), 2(z-3)>
then at the point P=(3,3,5), we get the gradient is equal to:
del S at (3,3,5)= <4,4,4>

We now can find the quation of the plane:

4(x-3)+4(y-3)+4(z-5)=0
Simplify:
4x-12+4y-12+4z-20=0
4x+4y+4z=44
x+y+z=11 <-- that is the equation of the plane

and the normal line is: <1,1,1>
equation to the normal line in the symmetric form:
X-3=y-3=z-5

Thanks Hero anyways, if you come back and you see this.