If a variable tangent to the curve `x^(2)y = c^(3)` makes intercepts a, b on x-and y-axes, respectively, then the value of `a^(2)b` is a)`27 c^(3)` b)`(4)/(27) c^(3)` c)`(27)/(4) c^(3)` d)`(4)/(9) c^(3)`

Options

A. `27 c^(3)`
B. `(4)/(27) c^(3)`
C. `(27)/(4) c^(3)`
D. `(4)/(9) c^(3)`

Answer

C