求下列各圆的方程(1)圆心为点C(8,-3),且过点A(5,1)(2)过A(-1,5),B(5,5),C(6,-2)三点
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求下列各圆的方程
(1)圆心为点C(8,-3),且过点A(5,1)
(2)过A(-1,5),B(5,5),C(6,-2)三点
(1)圆心为点C(8,-3),且过点A(5,1)
(2)过A(-1,5),B(5,5),C(6,-2)三点
圆心为点C(a,b),半径为 r 的圆的方程式:(x-a)^2 + (y-b)^2 = r^2
1.圆心为点C(8,-3),(x-8)^2 +(y+3)^2 = r^2
且过点A(5,1),(5-8)^2 +(1+3)^2 = r^2 = 25,r = 5
圆的方程式 = (x-8)^2 +(y+3)^2 = 25
2.过A(-1,5),B(5,5),C(6,-2)三点
(-1-a)² + (5-b)² = r² ---------(1)
(5-a)² + (5-b)² = r² ---------(2)
(6-a)² + (-2-b)² = r² ---------(3)
(2)-(1) a²-10a+25-a²-2a-1=0,a = 2,代进 (1),(3)
(4) 9 + (5-b)² = r² = b²-10b+25 +9 = b²-10b+34
(5) 16 + (-2-b)² = r² = b²+4b+4+16 = b²+4b+20
(4)-(5) -14b + 14 = 0,b = 1,代进 (4)
9 + 16 = r²,r = 5
(x - 2)² + (y - 1)² = 25
1.圆心为点C(8,-3),(x-8)^2 +(y+3)^2 = r^2
且过点A(5,1),(5-8)^2 +(1+3)^2 = r^2 = 25,r = 5
圆的方程式 = (x-8)^2 +(y+3)^2 = 25
2.过A(-1,5),B(5,5),C(6,-2)三点
(-1-a)² + (5-b)² = r² ---------(1)
(5-a)² + (5-b)² = r² ---------(2)
(6-a)² + (-2-b)² = r² ---------(3)
(2)-(1) a²-10a+25-a²-2a-1=0,a = 2,代进 (1),(3)
(4) 9 + (5-b)² = r² = b²-10b+25 +9 = b²-10b+34
(5) 16 + (-2-b)² = r² = b²+4b+4+16 = b²+4b+20
(4)-(5) -14b + 14 = 0,b = 1,代进 (4)
9 + 16 = r²,r = 5
(x - 2)² + (y - 1)² = 25
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