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Tardigrade
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Mathematics
Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2. Then the length of its latus rectum is
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Q. Let
H
be the hyperbola, whose foci are
(
1
±
√
2
,
0
)
and eccentricity is
√
2
. Then the length of its latus rectum is _____
JEE Main
JEE Main 2023
Conic Sections
A
3
B
5
2
C
2
D
3
2
Solution:
2
a
e
=
|
(
1
+
√
2
)
−
(
1
+
√
2
)
|
=
2
√
2
a
e
=
√
2
a
=
1
⇒
b
=
1
∵
e
=
√
2
⇒
Hyperbola is rectangular
⇒
L
⋅
R
=
2
b
2
a
=
2