若a^2+b^2=c^2,则直线ax+by+c=0被圆x^2+y^2=2所截得的弦长(...
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若a^2+b^2=c^2,则直线ax+by+c=0被圆x^2+y^2=2所截得的弦长(...
若a^2+b^2=c^2,则直线ax+by+c=0被圆x^2+y^2=2所截得的弦长(求过程)
若a^2+b^2=c^2,则直线ax+by+c=0被圆x^2+y^2=2所截得的弦长(求过程)
![若a^2+b^2=c^2,则直线ax+by+c=0被圆x^2+y^2=2所截得的弦长(...](/uploads/image/z/16355765-29-5.jpg?t=%E8%8B%A5a%5E2%2Bb%5E2%3Dc%5E2%2C%E5%88%99%E7%9B%B4%E7%BA%BFax%2Bby%2Bc%3D0%E8%A2%AB%E5%9C%86x%5E2%2By%5E2%3D2%E6%89%80%E6%88%AA%E5%BE%97%E7%9A%84%E5%BC%A6%E9%95%BF%EF%BC%88...)
a^x^2=(by+c)^2
x^2+y^2=1
(by+c)^2+a^2y^2-a^2=0
(a^2+b^2)y^2+2bcy+c^2-a^2=0
(y1-y2)^2=2a^2/(a^2+b^2)
b^y^2=(ax+c)^2
b^2x^2+(ax+c)^2-b^2=0
(x1-x2)^2=2b^2/(a^2+b^2)
弦长
=√[(y1-y2)^2+(x1-x2)^2]
=√[2a^2/(a^2+b^2)+2b^2/(a^2+b^2)]
=√[2(a^2+b^2)/(a^2+b^2)]
=√2
x^2+y^2=1
(by+c)^2+a^2y^2-a^2=0
(a^2+b^2)y^2+2bcy+c^2-a^2=0
(y1-y2)^2=2a^2/(a^2+b^2)
b^y^2=(ax+c)^2
b^2x^2+(ax+c)^2-b^2=0
(x1-x2)^2=2b^2/(a^2+b^2)
弦长
=√[(y1-y2)^2+(x1-x2)^2]
=√[2a^2/(a^2+b^2)+2b^2/(a^2+b^2)]
=√[2(a^2+b^2)/(a^2+b^2)]
=√2
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