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Find the equation of the hyperbola whose...

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

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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-0)^2+(y-3)^2}=2({x+y-1}/sqrt2)`
`implies (x-0)^2+(y-3)^2=4({x+y-1}/sqrt2)^2`
`implies x^2+y^2+9-6y=2(x^2+y^2+1+2xy-2y-2x)`
`implies x^2+y^2+4xy-4x+2y -7=0`
This is the required equation of the hyperbola.
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