Question

求两圆x^2+y^2-x+y-2=0及x^2+y^2=5的公共弦长.(不要联立,)

Answer 1

x^2+y^2-x+y-2=0

x^2+y^2=5

x-y=3

y=x-3

x^2+(x-3)^2=5

2x^2-6x+4=0

x^2-3x+2=0

x1=1,y1=-2

x2=2,y2=-1

弦长=√[(2-1)^2+(-1+2)^2]=√2