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Answer :

`"Vertex"-=(2,-2),"Focus"-=(2,-3//2),"Directrix":y=-(5)/(2)`Solution :

We have `x^(2)=2(2x+y)` <br> `:." "x^(2)-4x+4=2(y+2)` <br> `rArr" "(x-2)^(2)=2(y+2)` <br> Comparing with `(x-h)^(2)=2(y-k)`, we get <br> Vertex of the parabola is (2,-2). <br> Length of latus rectum =4a=2 <br> Axis of the parabola is x=2. <br> Also, parabola is concave upward. <br> Focus lies at distance a units above the vertex on the axis. <br> So, focus is `(2,-2+(1)/(2))-=(2,-(3)/(2))`. <br> Directrix is at distance a units below the vertex and perpendicular to the axis. <br> Therefore, directrix is `y=-2-(1)/(2)ory=-(5)/(2)`.