Focal Chord of Ellipse

Q.

PSQ is a focal chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}$ = 1 then $\frac{1}{SP}+\frac{1}{SQ}$ =

1. $\frac{2}{3}$

2. $\frac{3}{2}$

3. $\frac{4}{3}$

4. $\frac{4}{9}$

Q. If PSQ is a focal chord of the ellipse $16x^2+25y^2=400$ such that SP = 8 then the length of SQ =

1. 2
2. $\frac{11}{3}$
3. 16
4. 25

Q. PSP’ is a focal chord of the ellipse $16x^2+25y^2=400.$ If SP = 8 then SP’ =

1. $1$
2. $2$
3. $3$
4. $4$

Q. PSP’ is a focal chord of the ellipse $16x^2+25y^2=400.$ If SP = 8 then SP’ =

1. $1$
2. $2$
3. $3$
4. $4$

Q. The eccentric angles of extremities of a focal chord (other than Major axis) of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are ${\theta }_1$ and ${\theta }_2$.
If the eccentricity of the ellipse are $e_1$ and $e_2$ for the conditions $a>b$ and $b>a$ respectively, then ${\cos }^2\left(\frac{{\theta }_1-{\theta }_2}{2}\right)(\frac{1}{e_1^2}+\frac{1}{e_2^2})$ is