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Math Help - Intersection of hyperboloid with tangent plane

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    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.
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    Quote Originally Posted by mushroom View Post
    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?
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