If the center of the moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point------ Another problem: in the plane rectangular coordinate system xoy, two fixed points a and B on the parabola y2 = 4x which are different from the coordinate origin o are satisfied with AO vertical Bo, and the trajectory equation of the center of gravity g of the triangle AOB is obtained How to answer these two questions? How to find out?

If the center of the moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point------ Another problem: in the plane rectangular coordinate system xoy, two fixed points a and B on the parabola y2 = 4x which are different from the coordinate origin o are satisfied with AO vertical Bo, and the trajectory equation of the center of gravity g of the triangle AOB is obtained How to answer these two questions? How to find out?

First question:
X = - 2 is the directrix of the parabola. Let the focal point be p (the center of the circle is 0 on the parabola. According to the second definition, {OP} = | x + 2 |. The moving circle is tangent to x + 2 = 0. So OP} = | x + 2 | = the radius of the circle. The moving circle passes through the fixed point P (2,0)
Second question: let a (Ya ^ 2 / 4, ya) B (Yb ^ 2 / 4, Yb)
Substituting OA * ob = 0, we get: (Ya * Yb) ^ 2 / 16 + (Ya * Yb) = 0
yayb=-16
G [x, y], there are: x = (Ya ^ 2 / 4 + Yb ^ 2 / 4) / 3 = (Ya ^ 2 + Yb ^ 2) / 12
y^2=[(ya+yb)/3]^2=(ya^2+yb^2-32)/9
Easy to know: 12x = 8y ^ 2 + 32