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JEE Main Math Class 11 Coordinate Geometry Part 2 Questions
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© examsnet.com
Question : 58
Total: 100
If tangents are drawn to the ellipse
x
2
+
2
y
2
=
2
at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :
[Jan. 11, 2019 (I)]
1
4
x
2
+
1
2
y
2
=
1
x
2
4
+
y
2
2
=
1
1
2
x
2
+
1
4
y
2
=
1
x
2
2
+
y
2
4
=
1
Validate
Solution:
Given the equation of ellipse,
x
2
(
√
2
)
2
+
y
2
=
1
√
2
cos
θ
x
2
+
y
sin
θ
=
1
P
(
√
2
cos
θ
,
0
)
and
Q
(
0
,
1
sin
θ
)
Let mid point be
(
h
,
k
)
⇒
h
=
1
√
2
cos
θ
,
k
=
1
2
sin
θ
As
cos
2
θ
+
sin
2
θ
=
1
∴
1
2
h
2
+
1
4
k
2
=
1
Locus is
1
2
x
2
+
1
4
y
2
=
1
© examsnet.com
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