The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is
(A) y(dy/dx)2 + 4x(dy/dx) = 4y
(B) - y(dy/dx)2 = 2x(dy/dx) - y
(C) y(dy/dx)2 + y = 2xy(dy/dx)
(D) y(dy/dx)2 + 2xy(dy/dx) + y = 0
Answer is (B) - y(dy/dx)2 = 2x(dy/dx) - y
Equation of family of parabolas with focus at (0, 0) and the x-axis as axis is y2 = 4a(x + a). (1)
On differentiating Eq. (1) with respect to x,
