Find the equation of an ellipse whose focus is $(-1,1)$ eccentricity is $\large\frac{1}{2}$ and the directix is $x-y+3=0?$

Question

$\begin{array}{1 1}(a)\;7x^2+7y^2+2xy+10x-10y+7=0\\(b)\;7x^2-7y^2-2xy+10x-10y-7=0\\(c)\;7x^2+7y^2+2xy+10x+10y+10=0\\(d)\;x^2+y^2+2xy+10x-10y+7=0\end{array}$