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Joint Entrance Examination
Mathematics
Differential Equations
Question 327
Question 327 of 490
Medium
MCQ
The differential equation for the family of circles
x
2
+
y
2
−
2
a
y
=
0
x^2+y^2-2ay=0
x
2
+
y
2
−
2
a
y
=
0
(
a
a
a
arbitrary) is:
A
(
x
2
+
y
2
)
y
′
=
2
x
y
(x^2+y^2)y'=2xy
(
x
2
+
y
2
)
y
′
=
2
x
y
B
2
(
x
2
+
y
2
)
y
′
=
x
y
2(x^2+y^2)y'=xy
2
(
x
2
+
y
2
)
y
′
=
x
y
C
(
x
2
−
y
2
)
y
′
=
2
x
y
(x^2-y^2)y'=2xy
(
x
2
−
y
2
)
y
′
=
2
x
y
D
2
(
x
2
−
y
2
)
y
′
=
x
y
2(x^2-y^2)y'=xy
2
(
x
2
−
y
2
)
y
′
=
x
y
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Official solution
a
=
x
+
y
y
′
y
′
a=\dfrac{x+yy'}{y'}
a
=
y
′
x
+
y
y
′
; substituting into
x
2
+
y
2
−
2
a
y
=
0
x^2+y^2-2ay=0
x
2
+
y
2
−
2
a
y
=
0
gives
(
x
2
−
y
2
)
y
′
=
2
x
y
(x^2-y^2)y'=2xy
(
x
2
−
y
2
)
y
′
=
2
x
y
.
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