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Math Help - Line perpendicular to Paraboloid

  1. #1
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    Line perpendicular to Paraboloid

    Hi all,
    the problem is:
    Given the paraboloid P= 3x^2 + 2y^2 -2z = 1 and a point A(1,1,2) on it,
    find the line perpendicular to P at point A.

    I would appreciate any help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pqwerty View Post
    Hi all,
    the problem is:
    Given the paraboloid P= 3x^2 + 2y^2 -2z = 1 and a point A(1,1,2) on it,
    find the line perpendicular to P at point A.

    I would appreciate any help
    I don't have much time now, so I can't walk through the problem with you. here is the methodology though. hopefully it helps.

    Step 1:

    Find the tangent plane to the surface of the paraboloid at the point (1,1,2). This will be of the form ax + by + cz = d

    Step 2:

    Use the normal vector of the plane from step 1, this will be the vector <a,b,c>, as the direction vector for the line.

    Step 3:

    Write your solution. The line has the form:

    (1,1,2) + t<a,b,c>

    where t is a parameter. Write the line in the required form (the vector form, the symmetric form, or the parametric form)
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