x=acos(t), y=bsin(t); dx/dt=-asin(t), dy/dt=bcos(t), assuming a and b are constants.
Assuming s is arc length (measured along the curve), then incrementally:
ds²=dx²+dy² (Pythagoras),
(ds/dt)²=(dx/dt)²+(dy/dt)²=a²sin²(t)+b²cos²(t),
ds/dt=√(a²sin²(t)+b²cos²(t)).