Why does $b^2+a^2m^2=c^2$ in coordinate systems?

Question

I'm wondering how the formula above is derived. This is when the equation of an ellipse is $$(x^2/a^2)+(y^2/b^2)=1$$ and the tangent has an equation of $$y=mx+c$$

Answer 1

The first part of your equation is what we call the Pythagoras identity of the equation. To keep matters simple let a=b Sines and cosines are nothing but fractions of the hypotenuse anyways. That formula is Pythagoras theory in disguise.