# The equation of the ellipse whose focus is $(1,-1)$,the directrix the line $x-y-3=0$ and eccentricity $\large\frac{1}{2}$ is
$\begin{array}{1 1}7x^2+2xy+7y^2+10x-10y+7=0\\7x^2+2xy+7y^2+7=0\\7x^2+2xy+7y^2+10x-10y-7=0\\7x^2-2xy-7y^2-7=0\end{array}$