[tex]-2x+y^2-2y+5=0[/tex]
The standard form is given by:
[tex]\begin{gathered} y=Ax^2+Bx+C \\ or \\ x=Ay^2+By+C \end{gathered}[/tex]
Therefore:
[tex]x=\frac{y^2}{2}-y+\frac{5}{2}[/tex]
The vertex is the point V(h,k) which is given by:
[tex]\begin{gathered} k=\frac{-b}{2a} \\ h=y(k) \\ ---- \\ k=-\frac{-1}{2(\frac{1}{2})}=1 \end{gathered}[/tex][tex]y(1)=\frac{1^2}{2}+-1+\frac{5}{2}=2=h[/tex]
Therefore, the vertex is:
[tex]V=(2,1)[/tex]
the focus is:
[tex](3,1)[/tex]
And the directrix is:
[tex]x=1[/tex]
