Question:
If the co-ordinates of two points $\mathrm{A}$ and $\mathrm{B}$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $\mathrm{P}$ is any
point on the conic, $9 x^{2}+16 y^{2}=144$, then $\mathrm{PA}+\mathrm{PB}$ is equal to :
Correct Option: 1
Solution:
$\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$
$a=4 ; b=3 ; e=\sqrt{\frac{16-9}{16}}=\frac{\sqrt{7}}{4}$
$\mathrm{A}$ and $\mathrm{B}$ are foci
$\Rightarrow \mathrm{PA}+\mathrm{PB}=2 \mathrm{a}=2 \times 4=8$
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