The parabola x 2 = 4Y P is a tangent line of circle x 2 + (y + 1) 2 = 1 crossed by a moving point on the parabola passing through point P, y = - 2 at two points ab. when Pb is just tangent to the parabola and point P, the area of △ PAB is calculated

The parabola x 2 = 4Y P is a tangent line of circle x 2 + (y + 1) 2 = 1 crossed by a moving point on the parabola passing through point P, y = - 2 at two points ab. when Pb is just tangent to the parabola and point P, the area of △ PAB is calculated

Let P (a, b) B = a ^ 2 / 4
Then Pb: y = ax / 2-A ^ 2 / 4 = ax / 2-B
If the distance from the center of the circle to the straight line is 1, then we can get / B-1 / / the root sign (1 + b) = 1, then we can get b = 0 or 3 (0 is rounded off)
Since the two P are symmetric, let a > 0
Then a = 2 root sign 3
Let PA be y = K (X-2 radical 3) + 3
From the distance from the center of the circle to the straight line = 1, k = 5 root sign 3 / 11
A (- 5 / radical 3, - 2) B (1 / radical 3, - 2) P (2 radical 3,3)
The area is 5 pieces and 3 pieces