Focal Chord of Hyperbola

Q. If $\alpha$ and $\beta$ are the eccentric angles of the extremities of a focal chord of an ellipse of eccentricity e then $\cos \left(\frac{\alpha -\beta }{2}\right)=$

1. $e\cos \left(\frac{\alpha -\beta }{2}\right)$
2. $e\cos \left(\frac{\alpha +\beta }{2}\right)$
3. $e\cos \left(\frac{\alpha -\beta }{3}\right)$
4. $e\cos \left(\frac{2\alpha +2\beta }{2}\right)$

Q. If $\alpha$ and $\beta$ are the eccentric angles of the extremities of a focal chord of an ellipse of eccentricity e then $\cos \left(\frac{\alpha -\beta }{2}\right)=$

1. $e\cos \left(\frac{\alpha -\beta }{2}\right)$
2. $e\cos \left(\frac{\alpha +\beta }{2}\right)$
3. $e\cos \left(\frac{\alpha -\beta }{3}\right)$
4. $e\cos \left(\frac{2\alpha +2\beta }{2}\right)$