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Joint Entrance Examination
Mathematics
Differential Equations
Question 322
Question 322 of 490
Medium
MCQ
The differential equation of all circles through the origin with centres on the
x
x
x
-axis is:
A
y
2
=
x
2
+
2
x
y
d
y
d
x
y^2=x^2+2xy\dfrac{dy}{dx}
y
2
=
x
2
+
2
x
y
d
x
d
y
B
y
2
=
x
2
−
2
x
y
d
y
d
x
y^2=x^2-2xy\dfrac{dy}{dx}
y
2
=
x
2
−
2
x
y
d
x
d
y
C
x
2
=
y
2
+
x
y
d
y
d
x
x^2=y^2+xy\dfrac{dy}{dx}
x
2
=
y
2
+
x
y
d
x
d
y
D
x
2
=
y
2
+
3
x
y
d
y
d
x
x^2=y^2+3xy\dfrac{dy}{dx}
x
2
=
y
2
+
3
x
y
d
x
d
y
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Official solution
x
2
+
y
2
+
2
g
x
=
0
x^2+y^2+2gx=0
x
2
+
y
2
+
2
g
x
=
0
; eliminating
g
g
g
gives
y
2
=
x
2
+
2
x
y
d
y
d
x
y^2=x^2+2xy\dfrac{dy}{dx}
y
2
=
x
2
+
2
x
y
d
x
d
y
.
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