Eccentricity of a Conic

Q.

The equation of directrix of a conic is
$L:x+y-1=0$ and the focus is the point $(0,0)$. Find the equation of the conic if its eccentricity is
$\frac{1}{\sqrt{2}}$

1. $3x^2+3y^2+2xy+2x+2y-1=0$

2. $3x^2+3y^2+2xy+2x+2y+1=0$

3. $3x^2+3y^2+2xy-2x-2y+1=0$

4. $3x^2-3y^2+2xy+2x-2y+1=0$

Q.

P is a moving point, S is the focus and L is the directrix as shown in figure.

Which of the following represents the equation of a conic?

1. 

2. 

3. 

4.