I have complications to do the following problem:
A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors.
My first idea was to parameterize the curve given, however did not know how to introduce speed $v$. Therefore I derived with respect to time, the equation of the curve, obtaining:
$$2y\frac{\partial y}{\partial t}=-4a\frac{\partial x}{\partial t}$$
Also, I know that
$$\left( \frac{\partial y}{\partial t}\right)^2 +\left( \frac{\partial x}{\partial t}\right)^2=v^2$$
Thus have two equations relating the $x$ and $y$ components of the velocity, but I have not been able to resolve. Is my method OK? Is there another way? Is it easier to do so using the parametric equations, but then as I enter the speed $v$?