JEE Main 2020 (3 Sep, Shift 2) Maths Q65: Conic Sections

Question

Let

e_1

and

e_2

be the eccentricities of the ellipse,

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

(b < 5)

and the hyperbola,

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

respectively satisfying

e_1 e_2 = 1

. If

\alpha

and

\beta

are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair

(\alpha, \beta)

is equal to :

Official answer

Option 2

NTA final key (Sep 2020).

Accepted Answer

Option 2: $(8, 10)$

Answer

$\left(\frac{24}{5}, 10\right)$

Answer

$(8, 10)$

Answer

$\left(\frac{20}{3}, 12\right)$

Answer

$(8, 12)$

JEE Main 3 September 2020, Shift 2, Maths Q65