As shown in the figure, in the plane rectangular coordinate system xoy, it is known that the symmetry axis of the parabola is the Y axis, passing through (0,1), (- 4,5) two points 1 find the expression of the parabola 2. Given the coordinates (0,2) of point F, let the abscissa of any point P on the parabola be x0, make PM perpendicular to the x-axis at point m, connect PF, express the line segment PM and line segment PF with the formula containing x0, and compare the size of PM and PF 3 let the straight line PQ passing through point F intersect the parabola at another point Q. try to judge the position relationship between the circle with diameter PQ and the x-axis and explain the reason

As shown in the figure, in the plane rectangular coordinate system xoy, it is known that the symmetry axis of the parabola is the Y axis, passing through (0,1), (- 4,5) two points 1 find the expression of the parabola 2. Given the coordinates (0,2) of point F, let the abscissa of any point P on the parabola be x0, make PM perpendicular to the x-axis at point m, connect PF, express the line segment PM and line segment PF with the formula containing x0, and compare the size of PM and PF 3 let the straight line PQ passing through point F intersect the parabola at another point Q. try to judge the position relationship between the circle with diameter PQ and the x-axis and explain the reason

1. Let the parabolic equation be y = ax & # 178; + C (this is the parabolic equation with symmetry axis on Y axis) and substitute (0,1) (- 4,5) to get 1 = C 5 = 16A + 1 a = 1 / 4. The parabolic equation is y = x & # 178 / 4 + 12. The abscissa of P point is x0. The coordinates of y = x0 & # 178 / 4 + 1m point can be calculated as (x0,0) PM = | y | = | x0 & # 178 / 4 + 1 | pf & # 1