Question

Area of the segment cut off from the parabola $x^2=8y$ by the line $x-2y+8=0$ is:

• A. $12$
• B. $24$
• C. $48$
• D. $36$

Answer 1

The correct option is D $36$

$x^2=8y$ and $x-2y+8=0$
$x^2=4(x+8)$
$x^2-4x-32=0$
$x=-4;x=8$
area is
$\stackrel{8}{\underset{-4}{\int }}[\left(\frac{x+8}{2}\right)-\frac{x^2}{8}]dx$
$\stackrel{8}{\underset{-4}{\int }}(x/2+4-x^2/8)dx=\frac{x^2}{4}{|}_{-4}^8+4x{|}_{-4}^8-\frac{x^3}{24}{|}_{-4}^8$
$12+48-24$
$=36squnits$