I' m asked to find the plane equation for (x,y,z)-> 0,0,0.
I' m given the following function: $$f(x,y)=e^{x^{2}}+\ln(\frac{1}{xy})$$ Also the task specifies that the origin plane is parallel with the tangent plane and passes through the following point (x,y,z)->(1,1,e) (tangent plane)
I've found the tangent plane equation (after doing the partial derivatives) and the equation is :$$x(2e-1)+y-z-(e+2)=0$$ (Implicit form).
How do I find the plane passing through (0,0,0), origin, given that I have now the tangent plane equation? Can I just copy the coefficients and write 0 at the end since they are parallel? Like this perhaps: $$x(2e-1)+y-z=0$$