Question

If the area enclosed between the curves $y = kx^2$ and $x=ky^2$, $(k > 0)$, is $1$ square unit. Then $k$ is:

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

Answer 1

Answer: (A)

Area bounded by $y^2 = 4ax \; \& \; x^2 = 4by, a, b \neq 0$ is $\left| \frac{16ab}{3} \right|$
by using formula : $4a = \frac{1}{k} = 4b, k > 0 $
Area $= \left|\frac{16 . \frac{1}{4k} . \frac{1}{4k}}{3}\right| = 1 $
$ \Rightarrow k^{2} = \frac{1}{3} $
$\Rightarrow k = \frac{1}{\sqrt{3}} $