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BITSAT 2023 Shift 1 Solved Question Paper
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© examsnet.com
Question : 108
Total: 130
If the eccentricity and length of latus rectum of a hyperbola are
√
13
3
and
10
3
units respectively, then what is the length of the transverse axis?
7
2
unit
12 unit
15
2
unit
15
4
unit
Validate
Solution:
👈: Video Solution
Length of latus rectum of a hyperbola is
2
b
2
a
where
a
is the half of the distance between two vertex of the hyperbola.
Latus rectum
=
2
b
2
a
=
10
3
or,
b
2
=
5
a
3
. . . (i)
In case of hyperbola,
b
2
=
a
2
(
e
2
−
1
)
. . . (ii)
Putting value of
b
2
from equation (i) and
e
=
√
13
3
in equation (ii),
5
a
3
=
a
2
(
13
9
−
1
)
or,
5
a
3
=
4
a
2
9
⇒
4
a
2
−
15
a
=
0
or,
a
(
4
−
15
a
)
=
0
a
≠
0
, hence,
a
=
15
4
© examsnet.com
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