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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 97
Total: 100
If the normal at an end of a latus rectum of an ellipse passes through an extermity of the minor axis, then the eccentricity e of the ellipse satisfies:
[Sep. 06, 2020 (II)]
e
4
+
2
e
2
−
1
=
0
e
2
+
e
−
1
=
0
e
4
+
e
2
−
1
=
0
e
2
+
2
e
−
1
=
0
Validate
Solution:
Normal to the ellipse
x
2
a
2
+
y
2
b
2
=
1
at
(
a
e
,
b
2
a
)
is
a
2
x
a
e
−
b
2
y
b
2
∕
a
=
a
2
−
b
2
⇒
x
−
e
y
=
e
(
a
2
−
b
2
)
a
∵
(
0
,
−
b
)
lies on equation (i), then
b
e
=
e
(
a
2
−
b
2
)
a
⇒
a
b
=
a
2
e
2
⇒
b
=
a
e
2
⇒
b
2
a
2
=
e
4
∴
1
−
e
2
=
e
4
⇒
e
4
+
e
2
−
1
=
0
© examsnet.com
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