Known circle C: (x-3) ^ 2 + y ^ 2 = 100. A (- 3,0) Following title: P is any point of circle C, the vertical bisector l of line PA intersects PC at Q point, and the trajectory equation of Q point is obtained Make a straight line AB through the point P (1,1), which respectively intersects the positive half axis of X axis and the positive half axis of Y axis at two points a (a, 0). B (0, b). When a is the value, the area of triangle AOB is the smallest, and what is the minimum area?

Known circle C: (x-3) ^ 2 + y ^ 2 = 100. A (- 3,0) Following title: P is any point of circle C, the vertical bisector l of line PA intersects PC at Q point, and the trajectory equation of Q point is obtained Make a straight line AB through the point P (1,1), which respectively intersects the positive half axis of X axis and the positive half axis of Y axis at two points a (a, 0). B (0, b). When a is the value, the area of triangle AOB is the smallest, and what is the minimum area?

Because line L is the vertical bisector of line PA, and point q is on L, so PQ = aq. So QA + QC = PQ + QC = CP = 10. According to the definition of ellipse, point q is an ellipse with the sum of the distances to the fixed point (- 3,0) (3,0) of 10. That is, a = 5, C = 3, so B = 4, so the equation of locus ellipse of point q is x2 / 25 + Y2 / 16 = 1