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NIMCET 2024 Paper

Section: Mathematics

Question : 1 of 120

Marks: +1, -0

(4,3)

(12,5)

Solution:

We know that distance between the foci is

2 a e

and sum of the distances from any point on the ellipse from the two foci is

2 a

\;\; \text{Hence} \; \sqrt{(12-4)^2+(5-3)^2}=2 a e

\; \Rightarrow a e = \sqrt{17} \cdots (1)

Also

P S + P S' = 2 a

, here P is origin as the ellipse passes through origin.

\Rightarrow \sqrt{12^2+5^2} + \sqrt{4^2+3^2} = 2 a

a=9

. Putting the value of

a

in the first equation, we get

e = \frac{\sqrt{17}}{9}

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