# Thread: Intersection of hyperboloid with tangent plane

1. ## Intersection of hyperboloid with tangent plane

Find the intersection of the hyperboloid x^2 + y^2 - 3z^2 = 1 with its tangent plane at the point (2,0,1).

Equation of tangent plane: -2x + 3z = -1

Any clues? Thanks.

2. Originally Posted by mushroom
Find the intersection of the hyperboloid x^2 + y^2 - 3z^2 = 1 with its tangent plane at the point (2,0,1).

Equation of tangent plane: -2x + 3z = -1

Any clues? Thanks.
If you solve the equation of the tangent plane for z you get

$z=\frac{2x-1}{3}$ Now if you sub this into the equation for the hyperboloid and complete the square with respect to the x's what do you get?