在圖中,圓C1:X平方+Y平方-2X+6Y-15=0與X軸相交在A和B的2點

C1: x2 + y2 – 2x + 6y – 15 = 0
代y = 0,
x2 – 2x – 15 = 0
( x – 5 )( x + 3 ) = 0
x = 5 或 –3
所以AB 坐標分別是( 5 , 0 )和( - 3 ,0 )。
C2圓心: ( 1 , 0 ), 半徑: [ 5 – ( - 3 ) ] / 2 = 4
C2: ( x – 1 )2 + ( y – 0 )2 = 42
x2 + y2 – 2x – 15 = 0
C1圓心: ( 1 , - 3 )
代( 1 , - 3 )入C2,
L.H.S. = ( 1 )2 + ( - 3 )2 – 2 ( 1 ) – 15 = 8 – 15 = -7 ≠ 0
所以C2不穿過C1的圓心。

A ( 5 , 0 ), B ( - 3 , 0 )
x^2 + y^2 – 2x – 15 = 0
C2不穿過C1的圓心