Equation of plane question?

Find the equation of the tangent plane to the given surfaces at the point P.?

• I dont know how to go about this question: Find the equation of the tangent plane to the given surfaces at the point P. 1) z = xy, P = (-2, 1, -2) 2) z = x^2 - y^2, P = (3, 2, 5) And how do you go about this?

• Answer:

  Write the equation as a function of x,y, and z by moving z to the right hand side. f(x,y,z) = xy - z The normal vector will be the gradient of f evaluated at P. Once you do this, you'll have a point and a normal vector. This is all you need to write an equation for the tangent plane.