A particle moves along the curve `y=x^2+2xdot` At what point(s) on the curve are the `x` and `y` coordinates of the particle changing at the same rate?

Explanation

Equation of the curve,

`y = x^2+2x`

`:. dy/dt = 2x(dx/dt)+2(dx/dt)`

It is given that , `dx/dt = dy/dt`

`:. dx/dt = dx/dt(2x+2)`

`=>2x+2 = 1`

`=>x = -1/2`

`:. y = (-1/2)^2+2(-1/2)`

...