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JEE Main Math Class 11 Coordinate Geometry Part 3 Questions
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© examsnet.com
Question : 37
Total: 100
If a line along a chord of the circle
4
x
2
+
4
y
2
+
120
x
+
675
=
0
, passes through the point
(
−
30
,
0
)
and is tangent to the parabola
y
2
=
30
x
, then the length of this chord is
[2021, 26 Aug Shift-I]
5
7
5
√
3
3
√
5
Validate
Solution:
Equation of tangent to
y
2
=
30
x
is
y
=
m
x
+
30
4
m
Now, this tangent passes through
(
−
30
,
0
)
.
∴
0
=
−
30
m
+
30
4
m
⇒
30
4
m
=
30
m
⇒
m
2
=
1
4
⇒
m
=
±
1
2
∴
Equation of tangent is
y
=
x
2
+
15
or
y
=
−
x
2
−
15
Now equation of circle is
x
2
+
y
2
+
30
x
+
675
4
=
0
Let perpendicular distance of the tangent from the centre
(
−
15
,
0
)
of the circle
=
p
∴
p
=
|
−
15
2
+
15
|
√
1
+
1
4
=
3
√
5
∴
Length of chord
=
2
√
r
2
−
p
2
=
2
√
(
15
2
+
0
−
675
4
)
−
45
=
3
√
5
where,
r
is radius of the given circle.
© examsnet.com
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