Find the equation of the ellipse whose eccentricity is 1/2, the focus is `(1,1)` and the directrix is `x-y+3=0.`

Explanation

Let P≡(h,k) be moving point
`e=(PS)/(PM)​=1/2​`

`⇒(h+1)^2+(k−1)^2=1/4​((h−k+3​)/sqrt(2))^2`

`⇒` locus of P(h, k) is
`=>8(x^2+y^2+2x−2y+2)=(x^2+y^2−2xy+6x−6y+9)`

`=>7x^2+7y^2+2xy+10x−10y+7=0`