The equation of family of a curve is `y^(2)=4a(x+a),` then differential equation of the family is

Options

A. `y = y'+x`
B. `y =y''+x`
C. `y = 2y'x+yy'^(2)`
D. `y''y'+y^(2)=0`

Answer

a

Explanation

Given , ` y^(2) = 4ax + 4a^(2)" "` …(i)
On differentiating w.r.t.'x' ,we get
` rArr 2yy'= 4a`
On putting the value of 4a in Eq. (i) , we get
` y^(2) = 2yy'x +4 *(y^(2)y'2)/4`
` rArr y = 2y'x + yy'^(2)`