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JEE Advanced 2018 Paper 1
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© examsnet.com
Question : 52
Total: 54
Let ܲ be a point on the circle ܵS with both coordinates being positive. Let the tangent to ܵS at P ܲ intersect the coordinate axes at the points M and ܰN. Then, the mid-point of the line segment MN ܰmust lie on the curve
(
x
+
y
)
2
=
3
x
y
x
2
3
+
y
2
3
=
2
4
3
x
2
+
y
2
=
2
x
y
x
2
+
y
2
=
x
2
y
2
Validate
Solution:
Tangent at
P
(
2
c
o
s
θ
,
2
s
i
n
θ
)
is
x
c
o
s
θ
+
y
s
i
n
θ
=
2
M
(
2
s
e
c
θ
,
0
)
and
N
(
0
,
2
c
o
s
e
c
θ
)
Let midpoint be
(
h
,
k
)
h
=
s
e
c
θ
,
k
=
c
o
s
e
c
θ
1
h
2
+
1
k
2
=
1
1
x
2
+
1
y
2
=
1
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