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KEAM 2019 Math Paper
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© examsnet.com
Question : 30
Total: 121
The differential equation of all circles passing through origin and having their centres on the
X
-axis is
x
2
=
y
2
−
2
x
y
d
y
d
x
y
2
=
x
2
−
2
x
y
d
y
d
x
x
2
=
y
2
+
2
x
y
d
y
d
x
y
2
=
x
2
+
2
x
y
d
y
d
x
None of these
Validate
Solution:
Equation of any circle passing through origin and having their centres on the
X
-axis is
x
2
+
y
2
+
2
g
x
=
0
Differentiating,
x
+
y
d
y
d
x
+
g
=
0
g
=
−
y
d
y
d
x
−
x
=
−
(
x
+
y
d
y
d
x
)
Putting
g
in the equation.
x
2
+
y
2
−
2
x
(
x
+
y
d
y
d
x
)
=
0
Solving we get,
y
2
=
x
2
+
2
x
y
d
y
d
x
© examsnet.com
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