The plane equation passing through point (1,2, - 1) and parallel to plane 2x + 3y-z = 0 is

The plane equation passing through point (1,2, - 1) and parallel to plane 2x + 3y-z = 0 is

The obtained plane is: 2x + 3y-z = m, substituting point (1,2, - 1) to get: M = 9, then the obtained plane is:
2x＋3y－z=9

Find the plane equation of the intersection of point m (1, - 2,3) and two planes 2x-3y + Z = 3, x + 3Y + 2Z + 1 = 0?

(2x-3y+z-3)+a(x+3y+2z+1)=0
(2+6+3-3)+a(1-6+6+1)=0
a=-4
(2x-3y+z-3)-4(x+3y+2z+1)=0
2x+15y+7z+7=0

In the rectangular coordinate plane, the coordinate of the point on the x-axis whose distance to point a (1,2) is the root sign 5 is on the y-axis whose distance to point a (1,2) is the root sign 5
The coordinates of the point with root 2 are

The coordinates of the point on the x-axis whose distance to point a (1,2) is the root 5 are (0,0) or (2,0);
On the Y-axis and the distance to point a (1,2) is (0,0) or (0,4)

It is known that the difference between the distance from a moving point P to the point F (1,0) and the distance from the point P to the y-axis in the plane is equal to 1
It is known that the difference between the distance from a moving point P to point F (1,0) and the distance from point P to y axis is equal to 1
(I) the equation for finding the locus C of the moving point p;
(II) through point F, make two straight lines L1 and L2 whose slopes exist and are perpendicular to each other. Let L1 and trajectory C intersect at points a, B, L2 and trajectory C intersect at points D, e, and find the minimum value of adeb
This is the penultimate question of which simulation paper?

(1) ∵ the difference between the distance from a moving point P to point F (1,0) and the distance from point P to y axis in the plane is equal to 1 ∵ when x ≥ 0, the distance from point P to f is equal to the distance from point P to line x = - 1, ∵ the trajectory of moving point P is a parabola, and the equation is y2 = 4x (x ≥ 0). When x < 0, y = 0 ∵ the path C of moving point P is y2 = 4x (x ≥ 0) or

If the distance from point P to point F (4,0) is equal to the distance from point P to y axis, then the trajectory equation of point P is obtained

If the distance from point P (x, y) to point F (4,0) is equal to the distance from point P to y axis, then the trajectory equation of point P is obtained
(x-4) &# 178; + Y & # 178; = x & # 178;, which is reduced to Y & # 178; - 8x + 16 = 0, that is, Y & # 178; = 8x-16 (x ≥ 2). This is the trajectory equation of point P