The area bounded by = 4ax and y = mx is a^2 3 sq. units then m:

MCQ

The area bounded by $= 4ax$ and $y = mx$ is $\frac{\text{a}^2}{3}\text{sq. units}$ then $m:$

A
$1$
✓
$2$
C
$3$
D
$4$

✓

Answer

Correct option: B.

$2$

The two curves $y^2=4 a x$ and $y = mx$ intersect at
$=\Big(\frac{4\text{a}}{\text{m}^2},\frac{4\text{a}}{\text{m}}\Big)$ and the area enclosed by the two curves are given by
$=\int\limits^\frac{4\text{a}}{\text{m}2}_0\Big(\sqrt{4\text{ax}}-\text{mx}\Big)\text{dx}$
$\therefore\int\limits^\frac{4\text{a}}{\text{m}^2}\Big(\sqrt{4\text{ax}}-\text{mx}\Big)\text{dx}=\frac{\text{a}^2}{3}$
$\Rightarrow\frac{8}{3}.\frac{\text{a}^2}{\text{m}^3}=\frac{\text{a}^2}{3}$
$\Rightarrow\text{m}^3=8$
$\Rightarrow\text{m}=2$

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