已知圆方程X²+Y²=25,当m为何值时,直线4x-3y+m=0与圆相交?相切?相离
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![已知圆方程X²+Y²=25,当m为何值时,直线4x-3y+m=0与圆相交?相切?相离](/uploads/image/z/8628505-25-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%86%E6%96%B9%E7%A8%8BX%26%23178%3B%2BY%26%23178%3B%3D25%2C%E5%BD%93m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E7%9B%B4%E7%BA%BF4x-3y%2Bm%3D0%E4%B8%8E%E5%9C%86%E7%9B%B8%E4%BA%A4%3F%E7%9B%B8%E5%88%87%3F%E7%9B%B8%E7%A6%BB)
已知圆方程X²+Y²=25,当m为何值时,直线4x-3y+m=0与圆相交?相切?相离
已知圆方程X²+Y²=25,当m为何值时,直线4x-3y+m=0与圆相交?相切?相离
已知圆方程X²+Y²=25,当m为何值时,直线4x-3y+m=0与圆相交?相切?相离
d=|m|/5
d
x^2+y^2=25 (1)
4x-3y+m=0 (2)
sub (2) into (1)
[(3y-m)/4]^2 +y^2 =25
[(3y-m)]^2 +16y^2 =400
25y^2-6my +m^2-400=0
△ = 36m^...
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x^2+y^2=25 (1)
4x-3y+m=0 (2)
sub (2) into (1)
[(3y-m)/4]^2 +y^2 =25
[(3y-m)]^2 +16y^2 =400
25y^2-6my +m^2-400=0
△ = 36m^2- 100(m^2-400)
= -64m^2+40000
相交
△>0
-64m^2+40000 >0
m^2-625<0
-25
△=0
m=25 or -25
相离
△<0
m>25 or m<-25
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