question_answer

Area bounded by the parabola \[{{y}^{2}}=4ax\] and its latus rectum is                                  [RPET 1997, 2000, 02]

A)            \[\frac{2}{3}{{a}^{2}}\]sq. unit                                         

B)            \[\frac{4}{3}{{a}^{2}}\]sq. unit

C)            \[\frac{8}{3}{{a}^{2}}\]sq. unit                                         

D)            \[\frac{3}{8}{{a}^{2}}\]sq. unit

Correct Answer: C

Solution :

           Area = \[2\int_{0}^{a}{\,\,y\,dx=2\int_{0}^{a}{\sqrt{4ax}}\,\,dx}\]            \[2\times 2\sqrt{a}\times \frac{2}{3}\left| {{x}^{3/2}} \right|_{0}^{a}=\frac{8}{3}{{a}^{2}}\] sq. unit.