Given the point a (3,2), the line L: x + 2y-3 = 0. Find the minimum area of the triangle bounded by the point a and the positive half axis of the two coordinate axes and the linear equation at this time

Given the point a (3,2), the line L: x + 2y-3 = 0. Find the minimum area of the triangle bounded by the point a and the positive half axis of the two coordinate axes and the linear equation at this time

Because there is an intersection point between a straight line and two positive semiaxes, let the linear equation be y = ax + B, where a0x = 0, y = by = 0, x = - B / A, triangle s = - B ^ 2 / 2a, and a is on the straight line, so 2 = 3A + BB = 2-3as = - (2-3a) ^ 2 / 2A = 1 / 2 [- (9a ^ 2-12a + 4) / a] = 1 / 2 (- 9A + 12-4 / a) > = 1 / 2 (12 + 2 * 3 * 2) = 12, so the minimum area