The equation of the parabola whose focus is `(1, 1)` and the directrix is `x+y+1=0`

Explanation

We have given focus `= (1,1)` & equation of directrix `=x+y+1=0`

Now we have to find equation of parabola

Now, let `P(x,y)` be the Point on the parabola

So, PN be a perpendicular from P on the directrix.

then, we have `(SP)^2=(PN)^2`

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

`x^2+1-2x+y^2+1-2y= ((x+y+1)^2)/2`

`2x^2+2y^2+1-2x+1-2y=x^2+y^2+2xy+1+2x+2y`

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