In the rectangular coordinate plane, the distance from a moving point P on the right side of the y-axis to the point (1 / 2,0) is 1 / 2 larger than the distance from it to the y-axis The equation for finding the locus C of the moving point P Let Q be a moving point on the curve C, and the points B and C are on the y-axis. If the triangle QBC is a circumscribed triangle of circle (x-1) ^ 2 + y ^ 2, the minimum area of the triangle QBC is obtained

In the rectangular coordinate plane, the distance from a moving point P on the right side of the y-axis to the point (1 / 2,0) is 1 / 2 larger than the distance from it to the y-axis The equation for finding the locus C of the moving point P Let Q be a moving point on the curve C, and the points B and C are on the y-axis. If the triangle QBC is a circumscribed triangle of circle (x-1) ^ 2 + y ^ 2, the minimum area of the triangle QBC is obtained

(1) The distance from a moving point P on the right side of y-axis to f (1 / 2,0) is 1 / 2 greater than that from it to y-axis. Then | PF | is equal to the distance to the straight line x = - 1 / 2. Then the trajectory of point P is a parabola with F as the focus and x = - 1 / 2 as the guide line. The equation is y ^ 2 = 2x (2). Let Q (m, n), then n ^ 2 = 2m, make two circles (x-1) ^ 2 + y ^ 2 = 1