Find the equation of the parabola whose: focus is (0,0) and the directrix `2x-y-1=0`

Explanation

We have given focus `= (0,0)` & equation of directrix `=2x−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−0)^2+(y−0)^2=((2x−y-1)/sqrt(2^2+(−1)^2))^2`

`x^2+y^2= ((2x−y-1)^2)/5`

`5x^2+5y^2=4x^2+y^2−4xy+1+4x−2y`

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