NIMCET 2024 Paper

Section: Mathematics

Question : 1 of 120

Marks: +1, -0

(4,3)

and

(12,5)

are the two foci of an ellipse passing through the origin, then the eccentricity of the ellipse is:

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 "\; {√{ }}(12-4)^2+(5-3)^2=2 a e

\;⇒ a e={√{ }} 17 . . . . . . . . .(1)

Also

P S+P S^{'}=2 a

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

⇒ {√{ }} 12^2+5^2+{√{4^2+3^2}}=2 a

a=9

. Putting the value of

a

in the first equation, we get

e=\;{{√{17}}}/{9}

Go to Question:

Next Question