求解圆锥曲线的弦长公式的推导过程

2025-04-06 20:37:57
推荐回答(1个)
回答1:

y=kx+b
弦长d=√[(x1-x2)^2+(y1-y2)^2]
=√[(x1-x2)^2+k^2(x1-x2)^2]
=√(1+k^2)√[(x1-x2)^2]
=√(1+k^2)√[(x1+x2)^2-
4x1x2]
如果用y来表示
x=1/k(y-b)
就会得到d
=
√(1+k^2)[(x1+x2)^2
-
4x1x2]
=
√(1+1/k^2)[(y1+y2)^2
-
4y1y2]