1. ## Tangents and planes

Find the points on the ellipsoid

x^2 + 2y^2 + 3z^2 = 1

where the tangent plane is parallel to the plane

3x - y + 3z = 1

I have no idea how to do this, but i do have a knowledge of partial derivatives, its my first yr at university im 17.

2. ## Re: Tangents and planes

Originally Posted by Brennox
Find the points on the ellipsoid
$\displaystyle x^2 + 2y^2 + 3z^2 = 1$
where the tangent plane is parallel to the plane
$\displaystyle 3x - y + 3z = 1$
I have no idea how to do this, but i do have a knowledge of partial derivatives, its my first yr at university im 17.
You need to find the point(s) on the ellipsoid at which its gradient is parallel to the normal of the plane.

3. ## Re: Tangents and planes

Originally Posted by Plato
You need to find the point(s) on the ellipsoid at which its gradient is parallel to the normal of the plane.

yea and how do i do that??

4. ## Re: Tangents and planes

Originally Posted by Brennox
yea and how do i do that??
You first find the gradient to the surface. What is it?

5. ## Re: Tangents and planes

Originally Posted by Plato
You first find the gradient to the surface. What is it?
Ok im not rly sure what im doing but, do i find partial derivatives?

2x, 4y, 6z

then for 2nd eq its

3, -1, 3

If im not on the right track can you please show me the method

6. ## Re: Tangents and planes

Originally Posted by Brennox
Ok im not rly sure what im doing but, do i find partial derivatives
2x, 4y, 6z
then for 2nd eq its
3, -1, 3
Now you want $\displaystyle 2x=3t,~4y=-t,~\&^~6z=3t$.
Solve for $\displaystyle x,~y,~\&~z$ and substitute into the surface.
Solve for $\displaystyle t$.

7. ## Re: Tangents and planes

Originally Posted by Plato
Now you want $\displaystyle 2x=3t,~4y=-t,~\&^~6z=3t$.
Solve for $\displaystyle x,~y,~\&~z$ and substitute into the surface.
Solve for $\displaystyle t$.
So x = 3/2t, y = -1/4t and z = 1/2t

(3/2t)^2 + 2(-1/4t)^2 + 3(1/2t)^2 = 1 [eq 1]

9/2t + 1/4t + 3/2t = 1 [eq 2]

So is this right? if so.. after solving for t and finding the values of x,y and z is that my final answer? How do i know these are parallel?