Circle C: (x - a)^2 + (y - b)^2 = R^2(x−a)2+(y−b)2=R2
(a,b) in r: b = 2/3 a + 7(a,b)∈r:b=23a+7
C: (x - a)^2 + (y - 2/3 a - 7)^2 = R^2C:(x−a)2+(y−23a−7)2=R2
(3, 4) in C: (3 - a)^2 + (4 - 2/3 a - 7)^2 = R^2(3,4)∈C:(3−a)2+(4−23a−7)2=R2 // equation 1
(6, 4) in C: (6 - a)^2 + (4 - 2/3 a - 7)^2 = R^2(6,4)∈C:(6−a)2+(4−23a−7)2=R2 // equation 2
Subtract: (1) - (2)
(3 - a)^2 - (6 - a)^2 = 0(3−a)2−(6−a)2=0
3 - a = 6 - a3−a=6−a or 3 - a = - (6 - a)3−a=−(6−a)
0a = 30a=3 or 3 + 6 = a + a3+6=a+a
a = 9/2a=92
b = 2/3 * 9/2 + 7 = 10b=23⋅92+7=10
(1) \Rightarrow R^2 = (3 - 9/2)^2 + (4 - 10)^2⇒R2=(3−92)2+(4−10)2
R^2 = (3/2)^2 + 36 = (9 + 144)/4 = 153/4R2=(32)2+36=9+1444=1534