Ellipse has a focus $(3;0)$, a directrix $x+y-1=0$ and an eccentricity of $1/2$. Find its equation.
I should probably use the fact that $r/d = e$, where $r$ is the distance from the focus to any point $M(x,y)$ of an ellipse. $d$ the distance from $M(x,y)$ to the directrix, and $e$ is the eccentricity. However my attempt failed.