Tangent Plane
Explicit vs Implicit Surface Let’s say that you have a surface given by $z=f(x,y)$. You want to find the tangent plane to that surface at a given point $p_0 = (x_0, y_0, z_0)$. There are two tangent plane equations to choose from. The explicit equation $$ z = f(x_0, y_0) + f_x(x_0, y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0) $$ Or the implicit equation $$ 0 = \nabla f \cdot (p - p_0 ) $$ where $p = (x, y, z)$...