(x−a)2+(y−b)2=r2
(9−a)2+(33−b)2=r2
(27−a)2+(−15−b)2=r2
Eliminating r2
((9−a)2+(33−b)2)−((27−a)2+(−15−b)2)=0
(81−18a+a2+1089−66b+b2)−(729−54a+a2+225+30b+b2)=081+1089−729−225−18a+54a−66b−30b+a2−a2+b2−b2=0216+36a−96b=0
dividing through by 12 yields
3a−8b+18=0
Axle equation:
3y+2x−7=0.
it passes at (a,b)
hence
(3a−8b+18=0).2
(2a+3b−7=0).3
6a+9b−21=0
−
6a−16b+36=0
25b−57=0
b=57/25
2a+3∗(57/25)−7=0
2a−4/25=0
2a=4/25
a=2/25
Thus the center of the wheel is at (2/25,57/25)
Equation of the wheel becomes(x−2/25)2+(y−57/25)2=r2
now we must get radius r
one point on the circumference is A(9,33) ,center is C(2/25,57/25)
thus the radius is the magnitude of the distance between A and C
r2=((9−2/25)2+(33−57/25)2)=1023.2848
r=32units
hence equation of the circle becomes
(x−2/25)2+(y−57/25)2=322
Sketching this gives:
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