At this time, the distance from the center of the circle to the straight line is equal to the radius root number 8.

The x value at the intersection of the straight line and the x axis is m, and the absolute value of the intercept on the horizontal axis and the vertical axis is equal, forming an isosceles right triangle.

There are two such tangents, so m=4 or -4.

If you want to do hard work, so be it.

X=y+m, substitute x 2+y 2 = 8.

So (y+m) 2+y 2 = 8.

2*y^2+2my+2m^2-8=0

Using the discriminant of roots of binary linear equations

(2m)^2-4*(2m^2-8)*2=0

M=4 or -4