A particle travels along the parabola y=ax^2+x+b. At what point do its abscissa and ordinate change at the same rate?

Answer 1

dy/dt = 2ax dx/dt + dx/dt
dy/dt = dx/dt(2ax + 1)
but dy/dt = dx/dt , so
1 = 2ax + 1
2ax = 0
x = 0
then y = b
at the point (0,b)