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
Create a free account to view solution
View Solution FreeMore Differential Equation Questions
A curve passes through the point & its slope at any point is given by - cos2 . Then the curve has the equation -...The order and degree of the differential equation are -...The differential equation representing the family of curves y2 = 2c (x + √c), where c > 0, is a parameter, is of o...If = e-2y and y = 0 when x = 5, the value of x for y = 3 is...The differential equation of family of curve y = Aex + Be−x , where A and B are arbitrarily constants, is...