The area (in sq units) enclosed by the parabola y^2=8 x , its latus-rectum and the x -axis is

Step-by-step solution

The equation of the parabola is y^2 = 8x . Comparing this with y^2 = 4ax , we get 4a = 8 , which implies a = 2 . The latus-rectum of the parabola is the line x = a = 2 . The area enclosed by the parabola y^2 = 8x , the latus-rectum x = 2 , and the x -axis is given by the integral of y with respect to x from x = 0 to x = 2 . Since y^2 = 8x , we have y = 8x = 2 2 x . Area = ₀² 2 2 x dx = 2 2 ₀² x^ 1/2 dx . Evaluating the integral: 2 2 [ x^ 3/2 3/2 ]₀² = 2 2 2 3 [x^ 3/2 ]₀² . Area = 4 2 3 (2)^ 3/2 = 4 2 3 2 2 = 4 2 2