Question

The area enclosed by $y^2=4x$ and line $y=mx$ is equal to $2$ then the value of $m$ is

• A. $4$
• B. $2$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $2$


Point of contact,
$(mx{)}^2=4x\Rightarrow x=0;\frac{4}{m^2}$
The area enclosed,
$2=\underset{0}{\overset{\frac{4}{m^2}}{\int }}4xdx\Rightarrow 2=2[x^2{]}_0^{4/m^2}\Rightarrow 2=\frac{32}{m^4}\Rightarrow m=2$