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If the co-ordinates of two points A and B are \mathrm{(\sqrt{5}, 0)} and \mathrm{(-\sqrt{5}, 0)} respectively and P is any point on the conic, \mathrm{4 x^2+9 y^2=36}, then \mathrm{P A+P B} is equal to

Option: 1

4


Option: 2

6


Option: 3

8


Option: 4

9


Answers (1)

best_answer

We have, \mathrm{\frac{x^2}{9}+\frac{y^2}{4}=1}, i.e., \mathrm{\frac{x^2}{3^2}+\frac{y^2}{2^2}=1} 

which is an ellipse where \mathrm{a=3, b=2.}

\mathrm{ \therefore \quad e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{\frac{9-4}{9}}=\frac{\sqrt{5}}{3} }

So, A and B are foci.

\mathrm{ \Rightarrow \quad P A+P B=2 a=2 \times 3=6 }

Posted by

Ritika Harsh

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