1. The problem statement, all variables and given/known data "Find the equation of the plane tangent to the surface [itex] (x^2-y^2)(x^2+y^2)=15 [/itex] at the point [itex] (2,1) [/itex]" If only it really were a plane and a surface, I could do that. I have a formula for that. Unfortunately, this is a curve and I'm looking for tangent line. 2. Relevant equations In three dimensions, the formula for the equation of the tangent plane to the surface z=f(x,y) at the point [itex] P(x_0,y_0,z_0) [/itex] is [itex] z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0) [/itex] where [itex] f_a [/itex] is the partial derivative of f wrt a. 3. The attempt at a solution Well, pretending it's in three variables, I can do [tex] f_x=4x^3 [/tex] [tex] f_y=-4y^3 [/tex] [tex] z-z_0=f_x(2,1)(x-2)+f_y(2,1)(y-1) [/tex] [tex] z-z_0=32(x-2)-4(y-1) [/tex] So, how do I repair this situation/make the formula work in two dimensions/try something else?