JEE Mains 27-July-2022 Shift 1 Solved Paper

An ellipse E:‌

x2

a2

+‌

y2

b2

=1 passes through the vertices of the hyperbola H:‌

x2

49

−‌

y2

64

=−1. Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be ‌

1

2

. If l is the length of the latus rectum of the ellipse E, then the value of 113l is equal to ________.