Question

Area lying between the parabola $y^2=4ax$ and its latus rectum is

• A. $\frac{1}{3}a$ sq. units
• B. $\frac{1}{3}{a}^2$ sq. units
• C. $\frac{8}{3}a$ sq. units
• D. $\frac{8}{3}{a}^2$ sq. units

Answer 1

Answer: (D)

We have, $y^2=4ax$, parabola with vertex $(0,0)$ and focus $(a,0)$ and latus rectum $4a$.
Required area = area of shaded region
$A=2\underset{0}{\overset{a}{\int }}2\sqrt{a}\sqrt{x}dx$
$2{\left[2\sqrt{a}{x}^{3/2}\times \frac{2}{3}\right]}_0^a$

$=\frac{8}{3}{a}^2$ sq. units