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JEE Main Math Class 11 Coordinate Geometry Part 2 Questions
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© examsnet.com
Question : 51
Total: 100
If the normal to the ellipse
3
x
2
+
4
y
2
=
12
at a point
P
on it is parallel to the line,
2
x
+
y
=
4
and the tangent to the ellipse at P passes through Q (4,4) then
P
Q
is equal to :
[April 12, 2019 (I)]
5
√
5
2
√
61
2
√
221
2
√
157
2
Validate
Solution:
Slope of tangent on the line
2
x
+
y
=
4
at point
P
∣
is
1
2
Given ellipse is,
3
x
2
+
4
y
2
=
12
⇒
x
2
2
2
+
y
2
(
√
3
)
2
=
1
Let point
P
(
2
cos
θ
,
√
3
sin
θ
)
∴
equation of tangent on the ellipse, at
P
is,
x
2
cos
θ
+
y
√
3
sin
θ
=
1
⇒
m
T
=
−
√
3
2
cot
θ
∵
both the tangents are parallel
⇒
−
√
3
2
cot
θ
=
1
2
⇒
tan
θ
=
−
√
3
⇒
θ
=
π
−
π
3
or
θ
=
2
π
−
π
3
Case-1:
θ
=
2
π
3
,
then point
P
(
−
1
,
3
2
)
and
P
Q
=
5
√
5
2
Case-
2
:
θ
=
5
π
3
,
then tangent does not pass through
Q
(
4
,
4
)
© examsnet.com
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