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JEE Main Math Class 11 Coordinate Geometry Part 4 Questions
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© examsnet.com
Question : 42
Total: 100
The sum of diameters of the circles that touch (i) the parabola
75
x
2
=
64
(
5
y
−
3
)
at the point
(
8
5
,
6
5
)
and (ii) the
y
-axis, is equal to
[25-Jul-2022-Shift-1]
Your Answer:
Validate
Solution:
Equation of tangent to the parabola at
P
(
8
5
,
6
5
)
75
x
⋅
8
5
=
160
(
y
+
6
5
)
−
192
⇒
120
x
=
160
y
⇒
3
x
=
4
y
Equation of circle touching the given parabola at
P
can be taken as
(
x
−
8
5
)
2
+
(
y
−
6
5
)
2
+
λ
(
3
x
−
4
y
)
=
0
If this circle touches
y
-axis then
64
25
+
(
y
−
6
5
)
2
+
λ
(
−
4
y
)
=
0
⇒
y
2
−
2
y
(
2
λ
+
6
5
)
+
4
=
0
⇒
D
=
0
⇒
(
2
λ
+
6
6
)
2
=
4
⇒
λ
=
2
5
or
−
8
5
Radius
=
1
or 4
Sum of diameter
=
10
© examsnet.com
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