三　直线的参数方程

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基础巩固

1经过点M(2,7)且倾斜角为 π/6 的直线,以定点M到动点P的位移t为参数的参数方程是(　　)

A.{■(x=2"-" √3/2 t"," @y=7+1/2 t)┤(t为参数)B.{■(x=2+√3/2 t"," @y=7"-" 1/2 t)┤(t为参数)

C.{■(x=2"-" √3/2 t"," @y=7"-" 1/2 t)┤(t为参数)D.{■(x=2+√3/2 t"," @y=7+1/2 t)┤(t为参数)

解析根据直线参数方程的定义,得{■(x=2+tcos π/6 "," @y=7+tsin π/6)┤(t为参数),

即{■(x=2+√3/2 t"," @y=7+1/2 t)┤(t为参数).

答案D

2若直线的参数方程为{■(x=√3+1/2 t"," @y=3"-" √3/2 t)┤(t为参数),则该直线的斜率为(　　)

A.√3 B.-√3

C.√3/3 D.-√3/3

解析直线的参数方程为{■(x=√3+1/2 t"," @y=3"-" √3/2 t"," )┤化为标准形式{■(x=√3+"(-" t")" cos120"°," @y=3+"(-" t")" sin120"°" )┤(-t为参数),

所以直线的倾斜角为120°,斜率为-√3.

答案B

3(2018·北京朝阳区一模)若直线l的参数方程为{■(x="-" √3 t"," @y=1+3t)┤(t为参数),则l的倾斜角大小为(　　)

A.π/6 B.π/3

C. 2π/3 D.5π/6

解析由直线l的参数方程为{■(x="-" √3 t"," @y=1+3t)┤(t为参数),可知直线l的普通方程为y=1-√3 x,