Mathematics - Application of Derivative Question with Solution | TestHub

An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and a hyperbola $\frac{x^2}{{\alpha }^2}-\frac{y^2}{{\beta }^2}=1$ intersect orthogonally iff $a^2-b^2={\alpha }^2+{\beta }^2$. (A): $91-19=72=31+41✓$ (B): $71-17=54=31+23✓$ (C) and (D) don't intersect: the system of equations has no real solution (in (D) one ellipse lies wholly inside the other). So only (A) and (B) are correct.