Solution: estABlish a rectangular coordinate system with the center o of the semicircle as the coordinate origin and the straight line ab as the x axis, a
Solution: estABlish a rectangular coordinate system with the center o of the semicircle as the coordinate origin and the straight line ab as the x axis, as shown in the above figure.
then what The equation of semicircle o is: x? +y? = 1? ( 1≥y≥0)
Let the coordinates of point C be (a, b), then D(-a, b)? ,CD=2a? Among them? (0≤a≤ 1,0≤a≤ 1)
Substitute D(-a, b) into the semicircle O equation to get a? +b? = 1,b? = 1-a?
∵AD=BC=x? (x≥0)
∴x? =b? X for +( 1-a)? = 1-a? +( 1-a)? =2-2a,? 2a=2-x?
And AB=2.
∴y=2+2x+2-x? =? -? x? +2x+4
∫0≤a≤ 1,x=√(2-2a)
∴0≤x≤√2
∴y=-? x? +2x+4 (0≤x≤√2)