Let each of the two ellipses E₁: (x²)/(a²) + (y²)/(b²) = 1, (a > b) and E₂: (x²)/(A²) + (y²)/(B²) = 1, (A < B) have eccentricity 4/5. Let the lengths of the latus recta of E₁ and E₂ be l₁ and l₂, respectively, such that 2l₁² = 9l₂. If the distance between the foci of E₁ is 8, then the distance between the foci of E₂ is

Coordinate Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 24 Jan, Morning shift · Q9

JEE Main 202624 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let each of the two ellipses

E_1 : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

(a > b)

and

E_2 : \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1

(A < B)

have eccentricity

\frac{4}{5}

. Let the lengths of the latus recta of

E_1

and

E_2

l_1

and

l_2

, respectively, such that

2l_1^2 = 9l_2

. If the distance between the foci of

E_1

is 8, then the distance between the foci of

E_2