已知质点运动的轨迹方程为x=a+tcosθ,y=b+sinθ,t为参数,求质点从时间t1到t2经过的距离

x=a+tcosθ,y=b+tsinθ
x1=a+t1cosθ,y1=b+t1sinθ
M1(a+t1cosθ,b+t1sinθ)
x2=a+t2cosθ,y2=b+t2sinθ
M2(a+t1cosθ,b+t2sinθ)
|M1M2|=√[(x1-x2)²+(y1-y2)²]
=√[(t1-t2)²(cos²θ+sin²θ)]
=|t1-t2|
质点从时间t1到t2经过的距离|t1-t2|