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Byju's Answer
Standard XII
Mathematics
General Equation of Hyperbola
The latus rec...
Question
The latus rectum of the conic section
x
2
a
2
+
y
2
b
2
=
1
whose eccentricity =
e
is:
A
2
a
2
b
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B
2
b
a
2
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C
2
a
(
1
−
e
2
)
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D
2
b
(
1
−
e
2
)
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Solution
The correct option is
C
2
a
(
1
−
e
2
)
We know latus rectum of ellipse
x
2
a
2
+
y
2
b
2
=
1
is
2
l
=
2
b
2
a
Also for ellipse
b
2
=
a
2
(
1
−
e
2
)
⇒
2
l
=
2
a
(
1
−
e
2
)
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0
Similar questions
Q.
If the normal at the end of latus rectum of the ellipse
x
2
a
2
+
y
2
b
2
=
1
passes through
(
0
,
−
b
)
, then
e
4
+
e
2
(where
E
is eccentricity) equals
Q.
If the normal at the end of latus rectum of an ellipse
x
2
a
2
+
y
2
b
2
=
1
of eccentricity e passes through one end of the minor axis then
e
4
+
e
2
=
Q.
Statement-1 : Eccentricity of ellipse whose length of latus rectum is same as distance between is
2
s
i
n
18
o
Statement-2 : For
x
2
a
2
+
y
2
b
2
=
1
, eccentricity
e
=
√
1
−
b
2
a
2
Q.
If the equation to the circle, having double contact with the ellipse
x
2
a
2
+
y
2
b
2
=
1
(have eccentricity
e
) at the ends of a latus rectum, is
x
2
+
y
2
−
m
a
e
3
x
=
a
2
(
1
−
e
2
−
e
4
)
. Find
m
.
Q.
If the normal at the end of latus rectum of an ellipse
x
2
a
2
+
y
2
b
2
=
1
of eccentricity e passes through one end of the minor axis then
e
4
+
e
2
=
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