求过圆x平方+y平方-2x+2y+1=0与圆x平方+y平方+4x-2y-4=0的交点,圆心在直线x-2y-5=0的圆的方程

求过圆x平方+y平方-2x+2y+1=0与圆x平方+y平方+4x-2y-4=0的交点,圆心在直线x-2y-5=0的圆的方程
求过圆x平方+y平方-2x+2y+1=0与圆x平方+y平方+4x-2y-4=0的交点,圆心在直线x-2y-5=0的圆的方程

求过圆x平方+y平方-2x+2y+1=0与圆x平方+y平方+4x-2y-4=0的交点,圆心在直线x-2y-5=0的圆的方程
D:x^2+y^2-2x+2y+1=0.(1)
E:x^2+y^2+4x-2y-4=0.(2)
(2)-(1)两圆交点AB的直线方程:
AB:6x-4y-5=0
y=(6x-5)/4
x^2+(6x-5)^2/16-2x+2*(6x-5)/4+1=0
52x^2-44x+1=0
xA+xB=44/52=11/13,xA*xB=1/52
(xA-xB)^2=(xA+xB)^2-4xA*xB=(11/13)^2-4*1/52=108/169
AB^2=(xA-xB)^2+(yA-yB)^2=[1+(6/4)^2]*(xA-xB)^2=(52/16)*(108/169)=27/13
(AB/2)^2=27/52
D(1,-1),rC=1
E(-2,1),rD=3
DE:2x+3y+1=0.(3)
x-2y-5=0.(4)
C(-13,-9)
AB:6x-4y-5=0
h^2=|6*(-13)-4*(-9)-5|^2/(36+16)=2209/52
r^2=(AB/2)^2+h^2=27/52+2209/52=43
C:(x+13)^2+(y+9)^2=43
D:x^2+y^2-2x+2y+1=0.(1)
E:x^2+y^2+4x-2y-4=0.(2)
(2)-(1)两圆交点AB的直线方程:
AB:6x-4y-5=0
y=(6x-5)/4
x^2+(6x-5)^2/16-2x+2*(6x-5)/4+1=0
52x^2-44x+1=0
xA+xB=44/52=11/13,xA*xB=1/52
(xA-xB)^2=(xA+xB)^2-4xA*xB=(11/13)^2-4*1/52=108/169
AB^2=(xA-xB)^2+(yA-yB)^2=[1+(6/4)^2]*(xA-xB)^2=(52/16)*(108/169)=27/13
(AB/2)^2=27/52
D(1,-1),rC=1
E(-2,1),rD=3
DE:2x+3y+1=0.(3)
x-2y-5=0.(4)
C(-13,-9)
AB:6x-4y-5=0
h^2=|6*(-13)-4*(-9)-5|^2/(36+16)=2209/52
r^2=(AB/2)^2+h^2=27/52+2209/52=43
C:(x+13)^2+(y+9)^2=43
以上方法正确,请检验结果

D:x^2+y^2-2x+2y+1=0......(1)
E:x^2+y^2+4x-2y-4=0......(2)
(2)-(1)两圆交点AB的直线方程:
AB:6x-4y-5=0
y=(6x-5)/4
x^2+(6x-5)^2/16-2x+2*(6x-5)/4+1=0
52x^2-44x+1=0
xA+xB=44/52=11/13,xA*x...

全部展开

D:x^2+y^2-2x+2y+1=0......(1)
E:x^2+y^2+4x-2y-4=0......(2)
(2)-(1)两圆交点AB的直线方程:
AB:6x-4y-5=0
y=(6x-5)/4
x^2+(6x-5)^2/16-2x+2*(6x-5)/4+1=0
52x^2-44x+1=0
xA+xB=44/52=11/13,xA*xB=1/52
(xA-xB)^2=(xA+xB)^2-4xA*xB=(11/13)^2-4*1/52=108/169
AB^2=(xA-xB)^2+(yA-yB)^2=[1+(6/4)^2]*(xA-xB)^2=(52/16)*(108/169)=27/13
(AB/2)^2=27/52
D(1,-1),rC=1
E(-2,1),rD=3
DE:2x+3y+1=0......(3)
x-2y-5=0......(4)
C(-13,-9)
AB:6x-4y-5=0
h^2=|6*(-13)-4*(-9)-5|^2/(36+16)=2209/52
r^2=(AB/2)^2+h^2=27/52+2209/52=43
C:(x+13)^2+(y+9)^2=43
以上方法正确，请检验结果

收起