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Find the equation of the parabola whose ...

Find the equation of the parabola whose focus is at `(-1,-2)` and the directrix the line `x-2y+3=0`

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Given that, focus at `F(-1,-2)` and dirctrix is `x-2y+3=0`
Let any point on the parabola be `(x,y)`
`PF=abs((x-2y+3)/(sqrt(1+4)))`
`rArr (x+1)^(2)+(y+2)^(2)=((x-2y+3)^(2))/5`
`rArr5[x^(2)+2x+1+y^(2)+4y+4]=x^(2)+4y^(2)+9-4xy-12y+6x`
`rArr4x^(2)+y^(2)+4x+32y+16=0`
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