JEE Main202430 Jan 2024Morning ShiftMathematicsEllipseActual

If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

Options

A5 3
B3 2
C1 3
D2 5

Correct answer

D. 2 5

Step-by-step solution

The length of minor axis is given by 2 b and the distance between foci is given by 2 a e Given: 2 b = 1 2 × 2 a e ⇒ 2 b = a e ⇒ 4 b 2 = a 2 e 2 ⇒ 4 b 2 a 2 = e 2 ⇒ 4 1 - e 2 = e 2 ⇒ 4 - 4 e 2 = e 2 ⇒ e = 2 5

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