which one of the following is the differential equation to family of circles having centre at the origin ?

Options

A. `(x^(2) -y^(2)) (dy)/(dx) = 2xy `
B. ` (x^(2)+y^(2))(dy)/(dx) = 2xy`
C. `(dy)/(dx)= (x^(2) +y^(2))`
D. xdx + ydy =0

Answer

D

Explanation

The equation of family of circles having centres at the origin is
` x^(2) + y^(2)+r^(2)`
where 'r' is the radius.
Differentiate both sides w.r.t.x, we get
` 2x=2y (dy)/(dx) =0`
2x dx + 2y dy =0
` Rightarrow ` xdx + ydy =0
which is required differential equation.