求以点(2,-1)为圆心,且与直线2x+5y=0相切的圆的方程
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(2,-1)为圆心,圆的方程
(x-2)^2+(y+1)^2=r^2 (1)
2x+5y=0
y = -(2/5)x (2)
sub (2) into (1)
(x-2)^2+(y+1)^2=r^2
(x-2)^2 +(-(2/5)x+1)^2 =r^2
25(x-2)^2 +(2x-5)^2 =25r^2
29x^2-70x+125-25r^2=0
△=0
4900- 4(29)(125-25r^2)=0
4900-14500+2900r^2=0
r^2 = 9600/2900
=96/29
圆的方程: (x-2)^2+(y+1)^2=96/29
(x-2)^2+(y+1)^2=r^2 (1)
2x+5y=0
y = -(2/5)x (2)
sub (2) into (1)
(x-2)^2+(y+1)^2=r^2
(x-2)^2 +(-(2/5)x+1)^2 =r^2
25(x-2)^2 +(2x-5)^2 =25r^2
29x^2-70x+125-25r^2=0
△=0
4900- 4(29)(125-25r^2)=0
4900-14500+2900r^2=0
r^2 = 9600/2900
=96/29
圆的方程: (x-2)^2+(y+1)^2=96/29
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