My book states two seemingly contradicting statements for angle between conjugate diameters of an ellipse.
Conjugate diameters of the auxiliary circle are perpendicular to each other.
My question is, why? Is it an assumption? Or a statement?
Hence angle between corresponding conjugate diameters of an ellipse $\neq 90 ^\circ$
And then it goes ahead and states
The eccentric angles of the ends of pair of conjugate diameters differ by a right angle This last statement I have proved also using slopes.
Is there any difference between the angle of the conjugate diameters and the eccentric angle? What do they both represent visually?