JEE Main 2025 (7 Apr, Shift 2) Maths Q13: Conic Sections

Question

Let

e_1

and

e_2

be the eccentricities of the ellipse

\frac{x^2}{b^2}+\frac{y^2}{25}=1

and the hyperbola

\frac{x^2}{16}-\frac{y^2}{b^2}=1

, respectively. If

b<5

and

e_1e_2=1

, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :

(1) $\frac{\sqrt{3}}{2}$
(2) $\frac{\sqrt{7}}{4}$
(3) $\frac{3}{5}$ Official answer
(4) $\frac{4}{5}$

Official answer

Option 3

NTA final key.

Accepted Answer

Option 3: $\frac{3}{5}$

Answer

$\frac{\sqrt{3}}{2}$

Answer

$\frac{\sqrt{7}}{4}$

Answer

$\frac{3}{5}$

Answer

$\frac{4}{5}$

JEE Main 7 April 2025, Shift 2, Maths Q13

Same idea in other shifts