Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

let focus S(1,o) directrix x+ y +1 = 0 e = 1/root2. let P(x,y) be any point. M a point on the direc where the perpendicular from s meets the dir.

for an ellipse SP/PM = e

SP² / PM² = e²

( (x-1)² + y² ) / (x+y+1)²/2 = 1/2

x² - 2x + 1 + y² = 1/4 ( x²+y²+ 1 +2xy+2x+2y)C

4x² - 8x + 4 + 4y² = ( x²+y²+ 1 +2xy+2x+2y)

3x² + 3y² -2xy - 10x -2y + 3 = 0