Is it possible to create in WolframAlpha an animated plot of a curve given by an equation, where some of the coefficients depend on the parameter (=on time)?
For example if I would like to have a plot $x^2+2xy+3y^2+x+y=t$, which would show for each $t$ one of concentric ellipses and from the plot we could see how the curve changes when $t$ is changed. (The parameter $t$ stands for time.) Or a plot of $x^2+2xy-3y^2+x-y=t$, which could illustrate evolution of a family of hyperbolas.
Or is something like this possible only if I subscribe to the Pro version?
According to the help in Mathematica 10, you could do something like this:
ListAnimate[Table[WolframAlpha[StringJoin["contour plot x^2+2xy+3y^2+x+y==", ToString[t]]], {t,0,5,1}]]This shows a plot for each of the values $t=0,1,2,3,4,5$.