hi

I

1.Y=- 1.5X+6

(Needless to say, the problem 1, undetermined coefficient method)

2. Set point C coordinate (x, y)

Make a vertical line through point c, where CE is perpendicular to the x axis and the x axis intersects with e.

According to the fact that triangle BCE is similar to triangle ABO, CE/OB=BE/OA is obtained.

that is

y/t=(x-t)/6

(*)

Point M is the midpoint, and its coordinates can be easily obtained (t/2,3).

According to BM=BC

(x-t)^2+y^2=3^2+(t/2)^2

Simultaneous (*) formula, get

x=3+t

y=t/2

So the coordinates of point C (3+t, t/2)

The area of the triangle ABC = AB× BC/2 = 2× BC× BC/2 = BC 2 = (X-T) 2+Y 2 = 9+T2/4.

3.∫△ABD is an isosceles triangle.

∴∠BAD=∠ABD

∫OA//BD appears again.

∴∠OAB=∠ABD

∴∠OAB=∠BAD

Then it is easy to prove △OAB∽△BAC (because they are all right triangles).

∴BC/OB=AB/OA

that is

Number of roots (9+t 2/4)/t = 2× number of roots (9+t 2/4)/6

The solution is t=3.

At this time, the coordinate of b is (3,0).

(6 solutions, deceptive, more solutions)