购销网,兰州网站排名优化公司,网站翻页模板,网页设计要用到什么软件已知圆上两点P1#xff0c;P2#xff0c;坐标依次为 ( x 1 , y 1 ) , ( x 2 , y 2 ) (x_1,y_1),(x_2,y_2) (x1,y1),(x2,y2)#xff0c;圆的半径为 r r r#xff0c;求圆心的坐标。 假定P1#xff0c;P2为任意两点#xff0c;则两点连成线段的中点坐标是 x m i …已知圆上两点P1P2坐标依次为 ( x 1 , y 1 ) , ( x 2 , y 2 ) (x_1,y_1),(x_2,y_2) (x1,y1),(x2,y2)圆的半径为 r r r求圆心的坐标。 假定P1P2为任意两点则两点连成线段的中点坐标是 x m i d ( x 1 x 2 ) / 2 x_{mid} (x_1x_2)/2 xmid(x1x2)/2 y m i d ( y 1 y 2 ) / 2 y_{mid} (y_1y_2)/2 ymid(y1y2)/2 P1P2连线的斜率是 k ( y 1 − y 2 ) / ( x 1 − x 2 ) k (y_1-y_2)/(x_1-x_2) k(y1−y2)/(x1−x2) P1P2连线的垂线斜率为 m − 1 / k m -1/k m−1/k 则圆心所在的直线方程是 y − y m i d m ∗ ( x − x m i d ) y-y_{mid} m * (x - x_{mid}) y−ymidm∗(x−xmid)
圆心 ( x 0 , y 0 ) (x_0,y_0) (x0,y0)同时满足 ( x 0 − x 1 ) 2 ( y 0 − y 1 ) 2 r 2 (x_0-x_1)^2(y_0-y_1)^2r^2 (x0−x1)2(y0−y1)2r2和 y 0 − y m i d m ∗ ( x 0 − x m i d ) y_0-y_{mid} m * (x_0 - x_{mid}) y0−ymidm∗(x0−xmid) 或 ( x 0 − x 2 ) 2 ( y 0 − y 2 ) 2 r 2 (x_0-x_2)^2(y_0-y_2)^2r^2 (x0−x2)2(y0−y2)2r2和 y 0 − y m i d m ∗ ( x 0 − x m i d ) y_0-y_{mid} m * (x_0 - x_{mid}) y0−ymidm∗(x0−xmid)
将直线方程 y 0 m ∗ ( x 0 − x m i d ) − y m i d y_0 m*(x_0 -x_{mid})-y_{mid} y0m∗(x0−xmid)−ymid 代入圆的公式 得到 ( x 0 − x 1 ) 2 [ m ∗ ( x 0 − x m i d ) y m i d − y 1 ] 2 r 2 (x_0-x_1)^2[m * (x_0-x_{mid})y_{mid}-y_1]^2r^2 (x0−x1)2[m∗(x0−xmid)ymid−y1]2r2
展开 x 0 2 − 2 x 0 x 1 x 2 2 m 2 x 0 2 2 m x 0 ∗ ( y m i d − m ∗ x m i d − y 1 ) ( y m i d − m ∗ x m i d − y 1 ) 2 r 2 x_0^2-2x_0x_1x_2^2m^2x_0^22mx_0*(y_{mid}-m*x_{mid}-y_1)(y_{mid}-m*x_{mid}-y_1)^2r^2 x02−2x0x1x22m2x022mx0∗(ymid−m∗xmid−y1)(ymid−m∗xmid−y1)2r2
整理 ( 1 m 2 ) x 0 2 [ 2 m ( y m i d − m ∗ x m i d − y 1 ) − 2 x 1 ] ∗ x 0 ( y m i d − m ∗ x m i d − y 1 ) 2 x 1 2 − r 2 0 (1m^2)x_0^2[2m(y_{mid}-m*x_{mid}-y_1)-2x_1]*x_0(y_{mid}-m*x_{mid}-y_1)^2x_1^2-r^2 0 (1m2)x02[2m(ymid−m∗xmid−y1)−2x1]∗x0(ymid−m∗xmid−y1)2x12−r20
令 A 1 m 2 A 1m^2 A1m2 B 2 m ( y m i d − m ∗ x m i d − y 1 ) − 2 x 1 B 2m(y_{mid}-m*x_{mid}-y_1)-2x_1 B2m(ymid−m∗xmid−y1)−2x1 C ( y m i d − m ∗ x m i d − y 1 ) 2 x 1 2 − r 2 C (y_{mid}-m*x_{mid}-y_1)^2x_1^2-r^2 C(ymid−m∗xmid−y1)2x12−r2
则 x 0 − B ± B 2 − 4 A C 2 A x_0\frac{-B± \sqrt{B^2-4AC}}{2A} x02A−B±B2−4AC y 0 m ∗ ( x 0 − x m i d ) y m i d y_0 m*(x_0-x_{mid})y_{mid} y0m∗(x0−xmid)ymid
x_1 2
y_1 4
x_2 4
y_2 2
r 2
if (x_1 - x_2 0):print(横坐标相同求解可能出错)exit()
else:x_mid (x_1 x_2) / 2y_mid (y_1 y_2) / 2k (y_1-y_2)/(x_1-x_2)m -1/kA 1 m**2B 2 * m *(y_mid - m * x_mid - y_1)- 2 * x_1C (y_mid - m * x_mid - y_1)**2 x_1**2 - r**2print(A, B, C)x_c1 (-B ((B**2-4*A*C)**0.5))/(2*A)x_c2 (-B - ((B**2-4*A*C)**0.5))/(2*A)y_c1 m * (x_c1 - x_mid) y_midy_c2 m * (x_c2 - x_mid) y_midprint(圆心坐标,(x_c1,y_c1))print(圆心坐标,(x_c2,y_c2))运行结果 InsCode
