The area bounded by the parabola y^2=36 x and its latus rectum is

Step-by-step solution

The equation of the parabola is y^2 = 36x . Comparing this with the standard form y^2 = 4ax , we get 4a = 36 , which implies a = 9 . The latus rectum of the parabola is the line x = a = 9 . The points of intersection of the parabola y^2 = 36x and the latus rectum x = 9 are y^2 = 36(9) = 324 , so y = 18 . The area bounded by the parabola and its latus rectum is given by the integral A = 2 ₀⁹ y , dx = 2 ₀⁹ 36x , dx . A = 2 6 ₀⁹ x^ 1/2 , dx = 12 [ x^ 3/2 3/2 ]₀⁹ . A = 12 2 3 (9)^ 3/2 = 8 27 = 216 . Thus, the area is 2