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AIEEE 2007 Solved Paper
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© examsnet.com
Question : 107
Total: 118
The differential equation of all circles passing through the origin and having their centres on the
x
-axis is
y
2
=
x
2
+
2
x
y
d
y
d
x
y
2
=
x
2
−
2
x
y
d
y
d
x
x
2
=
y
2
+
x
y
d
y
d
x
x
2
=
y
2
+
3
x
y
d
y
d
x
Validate
Solution:
General equation of circles passing through origin
and having their centres on the
x
-axis is
x
2
+
y
2
+
2
g
x
=
0
....(i)
On differentiating w.r.t.x, we get
2
x
+
2
y
⋅
d
y
d
x
+
2
g
=
0
⇒
g
=
−
(
x
+
y
d
y
d
x
)
∴
equation
(
i
)
be
x
2
+
y
2
+
2
{
−
(
x
+
y
d
y
d
x
)
}
x
=
0
⇒
x
2
+
y
2
−
2
x
2
−
2
x
d
y
d
x
⋅
y
=
0
⇒
y
2
=
x
2
+
2
x
y
d
y
d
x
© examsnet.com
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