Find the equation of the ellipse whose focus is `(1,0),` the directrix is `x+y+1=0` and eccentricity is equal to `1/sqrt(2.)`

Explanation

Let S be the focus of the ellipse and e be the eccentricity of the ellipse.

Consider that P(x,y) be any point on the ellipse, then by the definition of ellipse,

`SP=exxPM`

`=>sqrt((x−1)^2+(y−0)^2)=1/sqrt(2)(x+y+1​)/sqrt(1^2+1^2)`


`=>sqrt((x−1)^2+(y)^2)​=1/2​(x+y+1)`

`=>(x−1)^2+(y)^2=1//4​(x+y+1)^2`

`=>3x^2+3y^2−2xy−10x−2y+3=0`

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