Question

x²+y²-4x+4y+6=0截直线x-y-5=0所得的弦长

Answer 1

x-y-5=0

x=y+5代和圆方程得

(y+5)^2+y^2-4(y+5)+4y+6=0

y^2+10y+25+y^2-4y-20+4y+6=0

2y^2+10y+11=0

y1+y2=10/2=5

y1y2=11/2

(y1-y2)^2=(y1+y2)^2-4y1y2

=5^2-4*11/2

=25-22

=3

(x1-x2)^2=(y1+5-y1-5)^2=(y1-y2)^2=3

∴弦长=√[(x1-x2)^2+(y1-y2)^2]=√(3+3)=√6