过圆O外一点M(a,b)向圆O:x方 y方=r方引两条切线,切点分别为A.B,求直线AB的方程有四五种解法,能都写出来么
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![过圆O外一点M(a,b)向圆O:x方 y方=r方引两条切线,切点分别为A.B,求直线AB的方程有四五种解法,能都写出来么](/uploads/image/z/6929652-12-2.jpg?t=%E8%BF%87%E5%9C%86O%E5%A4%96%E4%B8%80%E7%82%B9M%28a%2Cb%29%E5%90%91%E5%9C%86O%3Ax%E6%96%B9+y%E6%96%B9%3Dr%E6%96%B9%E5%BC%95%E4%B8%A4%E6%9D%A1%E5%88%87%E7%BA%BF%2C%E5%88%87%E7%82%B9%E5%88%86%E5%88%AB%E4%B8%BAA.B%2C%E6%B1%82%E7%9B%B4%E7%BA%BFAB%E7%9A%84%E6%96%B9%E7%A8%8B%E6%9C%89%E5%9B%9B%E4%BA%94%E7%A7%8D%E8%A7%A3%E6%B3%95%2C%E8%83%BD%E9%83%BD%E5%86%99%E5%87%BA%E6%9D%A5%E4%B9%88)
过圆O外一点M(a,b)向圆O:x方 y方=r方引两条切线,切点分别为A.B,求直线AB的方程有四五种解法,能都写出来么
过圆O外一点M(a,b)向圆O:x方 y方=r方引两条切线,切点分别为A.B,求直线AB的方程
有四五种解法,能都写出来么
过圆O外一点M(a,b)向圆O:x方 y方=r方引两条切线,切点分别为A.B,求直线AB的方程有四五种解法,能都写出来么
1,
(x-a)^2+(y-b)^2=(a^2+b^2)-r^2.(1)
x^2+y^2=r^2.(2)
(1)-(2):
AB:
2,
y-b=k*(x-a).(1)
x^2+y^2=r^2.(2)
(1),(2):
(1+k^2)x^2+2k(b-ka)x+(b-ka)^2-r^2=0
[2k(b-ka)]^2-4*(1+k^2)[(b-ka)^2-r^2]=0
kA= kB=
xA=k(ka-b)/(1+k^2),yA=
xB= yB=
k(AB)=(yA-yB)/(xA-xB)
AB:
3,
y-b=k(x-a)
kx-y+b-ka=0
d=r,d^2=r^2
|b-ka|^2/(1+k^2)=r^2
kA= kB=
AB:
4,
[(y-b)/(x-a)]*(y/x)=-1.(1)
x^2+y^2=r^2.(2)
xA= yA=
xB= yB=
k(AB)=
AB:
5,
切点(x,y):
OA:y=kx.(1)
x^2+y^2=r^2.(2)
(1),(2):
xA= yA=
xB= yB=
(yA/xA)*[(yA-b)/(xA-a)]=-1
kA= xA= yA=
kB= xB= yB=
6,
P(a,b)
k(AB)=-1/k(OP)=-a/b
AB:y=(-a/b)x+m.(1)
x^2+y^2=r^2.(2)
xA= yA=
xB= yB=
[(yA-b)/xA-a)]*(yA/xA)=-1
m=
[(yB-b)/(xB-b)]*(yB/xB)=-1
m=
AB:
7,
PA^2=PB^2=OP^2-r^2=a^2+b^2-r^2=
|PA|=|PB|=
∠AOP=arcsin(PA/OP)
k(OA)=
OA:y=kx.(1)
x^2+y^2=r^2.(2)
(1),(2)
xA= yA=
xB= yB=
AB: