求当m取何值时,直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0的交点到直线L3:4x-3y-12=0的距离最短?还有:这个最短距离是多少?快快快
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![求当m取何值时,直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0的交点到直线L3:4x-3y-12=0的距离最短?还有:这个最短距离是多少?快快快](/uploads/image/z/979195-67-5.jpg?t=%E6%B1%82%E5%BD%93m%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%2C%E7%9B%B4%E7%BA%BFL1%EF%BC%9A5x-2y%2B3m%283m%2B1%29%3D0%E4%B8%8EL2%3A2x%2B6y-3m%289m%2B20%29%3D0%E7%9A%84%E4%BA%A4%E7%82%B9%E5%88%B0%E7%9B%B4%E7%BA%BFL3%EF%BC%9A4x-3y-12%3D0%E7%9A%84%E8%B7%9D%E7%A6%BB%E6%9C%80%E7%9F%AD%3F%E8%BF%98%E6%9C%89%EF%BC%9A%E8%BF%99%E4%B8%AA%E6%9C%80%E7%9F%AD%E8%B7%9D%E7%A6%BB%E6%98%AF%E5%A4%9A%E5%B0%91%3F%E5%BF%AB%E5%BF%AB%E5%BF%AB)
求当m取何值时,直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0的交点到直线L3:4x-3y-12=0的距离最短?还有:这个最短距离是多少?快快快
求当m取何值时,直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0的交点到直线L3:4x-3y-12=0的距离最短?
还有:这个最短距离是多少?
快
快
快
求当m取何值时,直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0的交点到直线L3:4x-3y-12=0的距离最短?还有:这个最短距离是多少?快快快
求出交点为(3m,27m²/2+3m/2),交点坐标满足2y=3x²+x,则本题就是曲线y=(3/2)x²+(1/2)x上的点到直线4x-3y-12=0的最小距离.d=|4x-3y-12|/5=|(9/2)x²+(3/2)x-4x+12|/5=|9x²-5x+24|/10,求出最小值即可.
5x-2y+3m(3m+1)=0(1)
2x+6y-3m(9m+20)=0(2)
(1)×3+(2)
17x+9m(3m+1)-3m(9m+20)=0
17x=27m²+60m-27m²-9m
17x=51m
x=3m
代入(2)
6m+6y=3m(9m+20)
m+y=m(9m+20)/2
y=(...
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5x-2y+3m(3m+1)=0(1)
2x+6y-3m(9m+20)=0(2)
(1)×3+(2)
17x+9m(3m+1)-3m(9m+20)=0
17x=27m²+60m-27m²-9m
17x=51m
x=3m
代入(2)
6m+6y=3m(9m+20)
m+y=m(9m+20)/2
y=(9m²+18m)/2
到直线距离d=|12m-3/2(9m²+18m)-12|/5=3/10|-9m²-10m-8|=3/10|9(m+5/9)²+47/9|
=27/10(m+5/9)²+47/30
当m=-5/9时,d有最小值47/30
此时交点(-5/3,-65/18)
收起
5x-2y+3m(3m+1)=0(1)
2x+6y-3m(9m+20)=0(2)
(1)×3+(2)
17x+9m(3m+1)-3m(9m+20)=0
17x=27m²+60m-27m²-9m
17x=51m
x=3m
代入(2)
6m+6y=3m(9m+20)
m+y=m(9m+20)/2
y=(...
全部展开
5x-2y+3m(3m+1)=0(1)
2x+6y-3m(9m+20)=0(2)
(1)×3+(2)
17x+9m(3m+1)-3m(9m+20)=0
17x=27m²+60m-27m²-9m
17x=51m
x=3m
代入(2)
6m+6y=3m(9m+20)
m+y=m(9m+20)/2
y=(9m²+18m)/2
到直线距离d=|12m-3/2(9m²+18m)-12|/5=3/10|-9m²-10m-8|=3/10|9(m+5/9)²+47/9|
=27/10(m+5/9)²+47/30
当m=-5/9时,d有最小值47/30
此时交点(-5/3,-65/18)
收起
由L1,L2两方程式x=3m,y=5/4m平方,用点到直线的距离公式算