The differential equation of the family of hyperbolas having centres at the origin and whose axes are the coordinate axes is

Options

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

Answer

C