BITSAT 2023 Shift 1 Paper

Length of latus rectum of a hyperbola is ‌

2b2

a

where a is the half of the distance between two vertex of the hyperbola.
Latus rectum =‌

2b2

a

=‌

10

3

or, b2=‌

5a

3

. . . (i)
In case of hyperbola, b2=a2(e2−1) . . . (ii)
Putting value of b2 from equation (i) and e=
‌‌

√13

3

‌ in equation (ii), ‌‌

5a

3

=a2(‌

13

9

−1)‌ or, ‌
‌‌

5a

3

=‌

4a2

9

‌⇒4a2−15a=0‌ or, ‌a(4−15a)=0
‌‌‌a≠0‌, hence, ‌a=‌

15

4