The differential equation of family of curves of `y^(2)=4a(x+a)`is

Options

A. `y^(2)=4(dy)/(dx)((x+dy)/(dx))`
B. `2y (dy)/(dx)=4a`
C. `(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=0`
D. `2x(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)-y=0`

Explanation

Given that, `y^(2)=4a(x+a)…(i)`
On differentiating both sides w.r.t. x, we get
`2y(dy)/(dx)=4a Rightarrow 2y(dy)/(dx)=4a`
`Rightarrow y(dy)/(dx)=2a Rightarrow a=(1)/(2)y(dy)/(dx).........(ii)`
On putting the value of a form Eq. (ii) in Eq. (i) we get
`y^(2)=2y(dy)/(dx) (x+(1)/(s)y(dy)/(dx))`
`Rightarrow y^(2)=2xy(dy)/(dx)+y^(2)((dy)/(dx))^(2)`
`Rightarrow 2x(dy)/(dx)+y((dy)/(dx))^(2)-y=0`