Orthogonality of major and minor axes of an ellipse How would one go about proving that the major and minor axes of an ellipse are perpendicular bisectors of each other? I've read several proofs of expressions for the ellipse in cartesian and polar coordinates given the definition of the ellipse as the collection of points where the sum of the distance from two points is constant, but they always just assume that it is true. Visually it looks true, but is there an argument that follows simply from the definition?

As a very simple argument you can consider that an ellipse could be obtained by stretching a circle along a diameter, thus major and minor axes of an ellipse are perpendicular.

The reason for this is very clear considering the canonical form of an ellipse: $$\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1$$ which can be transformed in a circle stretching one axis. 
EG $$z=\frac{b}{a} y \to x^2+ z^2=a^2$$
This is also the reason for the formula to calculate the area of the ellipse $A=\pi ab$.
