If area bounded by the curves y2=4ax and y=mx is a23 t

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If area bounded by the curves

y^{2} = 4 a x a n d y = m x i s \frac{a^{2}}{3}

then the value of m is

Options:

A . 2

B . -2

C . 12

D . None of these

Answer: Option A
:
A
The two curves

y^{2}

= 4ax and y = mx intersect at

(\frac{4 a}{m^{2}}, \frac{4 a}{m})

and the area enclosed by the two curves is given by

\int_{0}^{\frac{4 a}{m^{2}}} (\sqrt{4 a x} - m x) d x

∴ \int_{0}^{\frac{4 a}{m^{2}}} (\sqrt{4 a x} - m x) d x = \frac{a^{2}}{3}

\Rightarrow \frac{8}{3} \frac{a^{2}}{m^{3}} = \frac{a^{2}}{3} \Rightarrow m^{3} = 8 \Rightarrow m = 2

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