A particle of mass $m$ moves under the influence of an attractive central force of magnitude $mk/r^2$ where $r$ is the distance from the origin.
I have the equations
$$ r^2\cdot \frac{d\theta}{dt} = h$$
and $$ \left(\frac{dr}{dt}\right)^2 + r^2\cdot \left(\frac{d\theta}{dt}\right)^2 - 2\frac kr = 2E $$
where $h$ and $E$ are constants of the motion.
And I need to verify that $r = a(1-e\cdot \cos(\theta))^-1$ is a solution of the above equations, finding conditions for $h$ and $E$ in terms of $k$,$e$,$a$.
Everytime I attempt this I have trouble eliminiating $\frac{dr}{dt}$ or $\frac{d\theta}{dt}$ so could anybody show me how to solve verify this?
Thanks