FInding Points of Tangent Line w/ Vectors

[Loppyfoot]

Homework Statement

Consider the ellipsoid 4x^2+2y^2+z^2 = 19. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 2y−8x+z = 0.

Homework Equations

The Attempt at a Solution

So I found the normal vector to the tangent, <8x,4y,2z>.

I also found the normal vector to the plane, <-8,2,1>

So what step do I do next? I'm Confused on where to go after this.

 

[tiny-tim]

Hi Loppyfoot!

(try using the X² icon just above the Reply box )

So I found the normal vector to the tangent, <8x,4y,2z>.

I also found the normal vector to the plane, <-8,2,1>

So what step do I do next? I'm Confused on where to go after this.

But you're there!

Just make the two parallel (ie in the same ratios), to find an equation for x/z and y/z, and then put them into the original ellipse equation to find the points on the actual ellipse.