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)