If x2+ y2=1, then :
(A) yy' - 2(y ' )2+1=0 (B) yy'' + (y ' )2+1=0
(C) yy = (y ' )2-1=0 (D) yy''+2(y ' )2+1=0

x^2 + y^2 = 1,

Differentiate w.r.t. x,

2x + 2yy' = 0,

Again differentiate,

2 + 2( yy'' +y'^2) = 0,

or, yy'' + y'^2 + 1 = 0,

ANS is (B).

differnciating x^2 + y^2 w.r.t.  x we get

2x + 2yy' = 0  or x + yy' = 0

again differenciating w.r.t x we get

1+y'y' + yy'' = 0 or 1 + (y')^2 + yy'' = 0

so answer is (B)