Question

If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7},0)$ and $(-\sqrt{7},0)$ respectively and $P$ is any point on the conic, $9x^2+16y^2=144$, then $PA+PB$ is equal to :

• A. $6$
• B. $16$
• C. $9$
• D. $8$

Answer 1

The correct option is D $8$

$\frac{x^2}{16}+\frac{y^2}{9}=1$
$a=4,b=3$
$e=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$
Focii are $F_1(\sqrt{7},0),F_2(-\sqrt{7},0)$
$P{F}_1+P{F}_2=2a$
$PA+PB=$ $2\times 4=8$