Differential EquationHard
Question
The differential equation of all circles passing through the origin and having their centres on the x-axis is
Options
A.x2 = x2 + xy 
B.x2 = x2 + 3xy
C.x2 = x2 + 2xy
D.x2 = x2 - 2xy
Solution
General equation of all such circles is
x2 + y2 + 2gx = 0.
Differentiating, we get
2x + 2y + 2g = 0
∴ Desired equation is
x2 + y2 +
x = 0
⇒ y2 = x2 + 2xy
x2 + y2 + 2gx = 0.
Differentiating, we get
2x + 2y
+ 2g = 0∴ Desired equation is
x2 + y2 +
x = 0 ⇒ y2 = x2 + 2xy
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