Archimedes proved that the area between a line and a parabola equals 4/3 the area of the inscribed triangle formed by the two pints of intersection and the point on the parabola midway between the x-values of those intersections. Find the area between the parabola defined by 64y= 144-x^2 and the line defined by 8y=3x-36.

Question

Archimedes proved that the area between a line and a  parabola equals 4/3 the area of the inscribed triangle formed by the two pints of intersection and the point on the parabola midway between the x-values of those intersections.  Find the area between the parabola defined by 64y= 144-x^2 and the line defined by 8y=3x-36.

sirm3d · Answer

(a) find the points of intersection of the line and the parabola
(b) get the average of the x-coordinates of the two points intersection
(c) use the value obtained in (b) to find the third point on the parabola

use any method you know to find the area of the triangle if the coordinates of the vertices are known.