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已知直线y=ax+b与圆x方+y

解:设M(x1,y1),N(x2,y2) y=ax+b x^2+y^2=1 x^2+(ax+b)^2=1 (a^2+1)x^2+2abx+b^2-1=0 x1+x2=-2ab/(a^2+1),x1*x2=(b^2-1)/(a^2+1) (x1-x2)^2=(x1+x2)^2-4x1x2=[(-2ab/(a^2+1))^2-4(b^2-1)]/(a^2+1)=4(a^2-b^2+1)/(a^2+1)^2 (y1-y2)^2=a^2(x1-x2)^2 MN^2=(x1-x2)^2+(y1-y2)^2=(a^2+1)(x1-x2)^2=4(a^2-b^2+1)/(a^2+1) OM^2=x1^2...全部

  解:设M(x1,y1),N(x2,y2) y=ax+b x^2+y^2=1 x^2+(ax+b)^2=1 (a^2+1)x^2+2abx+b^2-1=0 x1+x2=-2ab/(a^2+1),x1*x2=(b^2-1)/(a^2+1) (x1-x2)^2=(x1+x2)^2-4x1x2=[(-2ab/(a^2+1))^2-4(b^2-1)]/(a^2+1)=4(a^2-b^2+1)/(a^2+1)^2 (y1-y2)^2=a^2(x1-x2)^2 MN^2=(x1-x2)^2+(y1-y2)^2=(a^2+1)(x1-x2)^2=4(a^2-b^2+1)/(a^2+1) OM^2=x1^2+y1^2=1 ON^2=x2^2+y2^2=1 cos(A+B)=cos(360度-∠MON)=cos∠MON=(OM^2+ON^2-MN^2)/(2OM*ON) =[1+1-4(a^2-b^2+1)/(a^2+1)]/2 =(2b^2-a^2-1)/(a^2+1)。
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