If area bounded by the curve `y^(2)=4ax` and `y=mx` is `a^(2)//3` , then the value of m, is

Options

A. 2
B. `-2`
C. `1/2`
D. None of these

Answer

A

Explanation

The two curve ` y^(2) = 4ax and y = mx " intersect at " ((4a)/m^(2) , (4a)/m)` and the area enclosed by the two curves is given by
`int_(0)^(4a//m^(2)) (sqrt(4ax)-mx)dx`
` therefore int_(300)^(4a//m^(2)) (sqrt(4ax) -mx)dx=a^(2)/3`
`8/3 a^(2)/m^(3) = a^(2)/3`
` Rightarrow m^(3) =8`
` Rightarrow a=2`