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