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

Answer 1

The correct option is C $\frac{1}{\sqrt{3}}$


Required area = OABCO
${\int }_0^{1/a}(\sqrt{\frac{x}{a}}-a{x}^2)dx=1\Rightarrow a^2=\frac{1}{3}\Rightarrow a=\frac{1}{\sqrt{3}}$