Find the equation of the hyperbola whose : focus is (1,1) directrix is `2x+y=1` and eccentricity `=sqrt(3)`

Explanation

Let `P(x,y)` be a point on the hyperbola.

And we know that,

Distance of point `P` from focus`=` Eccentricity `xx` Distance of point `P` from directrix.

`therefore sqrt{(x-1)^2+(y-1)^2}=sqrt3({2x+y-1}/sqrt5)`

`implies (x-1)^2+(y-1)^2=3({2x+y-1}/sqrt5)^2`

`implies x^2+1-2x+y^2+1-2y=3/5(4x^2+y^2+4xy+1-4x-2y)`

`implies 5x^2+5y^2-10x-10y+10=12x^2+3y^2+12xy-12x-6y+3=0`

`implies 7x^2-2y^2+12xy-2x+4y-7=0`

...