求解圆锥曲线的弦长公式的推导过程
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求解圆锥曲线的弦长公式的推导过程
即下面的公式:d = √(1+k^2)[(x1+x2)^2 - 4x1x2] = √(1+1/k^2)[(y1+y2)^2 - 4y1y2]
即下面的公式:d = √(1+k^2)[(x1+x2)^2 - 4x1x2] = √(1+1/k^2)[(y1+y2)^2 - 4y1y2]
![求解圆锥曲线的弦长公式的推导过程](/uploads/image/z/17895371-59-1.jpg?t=%E6%B1%82%E8%A7%A3%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF%E7%9A%84%E5%BC%A6%E9%95%BF%E5%85%AC%E5%BC%8F%E7%9A%84%E6%8E%A8%E5%AF%BC%E8%BF%87%E7%A8%8B)
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]
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]