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Byju's Answer
Standard XII
Mathematics
Eccentricity of Hyperbola
The differenc...
Question
The difference between the lengths of the major axis and the latus-rectum of an ellipse is
(a) ae
(b) 2ae
(c) ae
2
(d) 2ae
2
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Solution
(
d
)
2
a
e
2
Length
of
the
latus
rectum
=
2
b
2
a
and
e
=
1
-
b
2
a
2
a
2
e
2
=
a
2
-
b
2
⇒
b
2
=
a
2
-
a
2
e
2
⇒
b
2
=
a
2
1
-
e
2
∴
Length
of
the
latus
rectum
=
2
a
2
1
-
e
2
a
=
2a(1-e
2
)
Length of the major axis=2a
Difference
between
length
of
latus
rectum
and
length
of
major
axis
=
2
a
-
2a(1-e
2
)
=
2
a
-
2
a
+
2
a
e
2
=
2
a
e
2
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Q.
The difference between the lengths of the major axis and the latus-rectum of an ellipse is
(a) ae
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B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis
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(
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√
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