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Circles are drawn with diameter being an...

Circles are drawn with diameter being any focal chord of the parabola `y^2-4x-y-4=0` with always touch a fixed line. Find its equation.

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`y^(2)-4x-y-4=0`
`ory^(2)-y+(1)/(4)=4x+(17)/(4)`
`or(y-(1)/(2))^(2)=4(x+(17)/(16))`
Circle drawn with diameter as extremities of any chord of the parabola always touches the directrix of the parabola.
Thus, the circle will touch the line
`x+(17)/(16)=-1`
`or16x+33=0`
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