Question

The area bounded by the parabola $y^2=8x$ and its latus rectum in sq unit is

• A. $16/3squnit$
• B. $32/3squnit$
• C. $8/3squnit$
• D. $64/3squnit$
• E. $4/3squnit$

Answer 1

Answer: (B)

The given equation of parabola is
$y^2=8x$ ...(i)
Required area
$=2{\int }_0^2\sqrt{8x}dx=2.2\sqrt{2}{\int }_0^2\sqrt{x}dx$
$=4\sqrt{2}{\left[\frac{x^{3/2}}{3/2}\right]}_0^2=4\sqrt{2}\left[\frac{2\sqrt{2}}{3/2}\right]$
$=\frac{32}{3}squnit$