Focal Chord of Ellipse

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. 
3. 16
4. 25

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. 2/3

2. 3/2

3. 4/3

4. 4/9

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

1. 
2. 
3. 
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

Q. An ellipse having foci at $(3,3)$ and $(-4,4)$ and passing through the origin has eccentricity equal to:

1. $\frac{3}{7}$
2. $\frac{2}{7}$
3. $\frac{5}{7}$
4. $\frac{3}{5}$

Q. On the ellipse, $9x^2+25y^2=225$, find the point whose distance to the focus $F_1$ is four times the distance to the other focus $F_2$.

1. $[-15,\sqrt{63}]$
2. $\left(\frac{-15}{4},\frac{\sqrt{63}}{2}\right)$
3. $\left(\frac{-15}{4},\frac{\sqrt{63}}{4}\right)$
4. $\left(\frac{-15}{2},\frac{\sqrt{63}}{2}\right)$

Q. The sum of the distances of any point on the ellipse $3x^2+4y^2=24$ from its foci is :

1. $8\sqrt{2}$
2. $16\sqrt{2}$
3. $4\sqrt{2}$
4. $8$

Q. Find the lengths of, and the equations to, the focal radii drawn to the point $(4\sqrt{3},5)$ of the ellipse $25x^2+16y^2=1600$.

Q. If $F_1=(3,0)$, $F_2=(-3,0)$ and $P$ is any point on the curve $16x^2+25y^2=400$, then $P{F}_1+P{F}_2$ equals to:

1. $8$
2. $6$
3. $10$
4. $12$

Q. Find the focal distance of a point $P\left(\theta \right)$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$