Question

The area enclosed between the curves $y=a{x}^2$ and $x=a{y}^2(a>0)$ is 1 sq. unit, then the value of a is

• A. $1/\sqrt{3}$
• B. $1/2$
• C. $1$
• D. $1/3$

Answer 1

The correct option is A $1/\sqrt{3}$

Points of intersection of $y=a{x}^2$ and
$x=a{y}^2$ are $(0,0)$ and
$\left(\frac{1}{a},\frac{1}{a}\right)$.
Hence area is, ${\int }_0^{1/a}(\sqrt{\frac{x}{a}}-a{x}^2)dx=1\Rightarrow a=\frac{1}{\sqrt{3}}(asa>0)$.