A General Conic Section is given by the equation $ax^2 + by^2 + 2hxy +2gx +2fy + c =0 $. Let the $\theta$ be the slope of one of its axes.
Prove that :
$$\tan 2\theta = \dfrac{2h}{a-b}$$
I tried to use the definition of the conic section by taking cases for various conics such as parabola, pair of straight lines, ellipse, hyperbola etc. but it became too tedious to calculate. Are there some properties with which this question can be simplified ?
Any help will be appreciated.
Thanks.