FInding Points of Tangent Line w/ Vectors

1. The problem statement, all variables and given/known data

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.





3. 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.

All right, now:



Equivalently:



Then, substitute that in the ellipsoide equation.

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Fernando Revilla

Thanks,

I got, (-2,1,1)
and (2,-1,-1)

All right.

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Fernando Revilla