The differential equation of family of curves `x^(2)+y^(2)-2ax=0`, is

Options

A. `x^(2) -y^(2) - 2xyy''=0`
B. `y^(2)-x^(2)=2xyy'`
C. `x^(2)+y^(2)+2y''=0`
D. None of the above

Answer

c

Explanation

Given , `x^(2) +y^(2) - 2ax = 0 " "` … (i)
On diferentiating w.r.t.'x' we get
` rArr 2 x + 2yy' - 2a = 0 `
` rArr a = x + y y'`
On putting the value of a in Eq. (i) , we get
`x^(2) + y^(2) - 2x (x+ yy') =0`
` rArr y^(2) - x^(2) = 2 xyy'`