first we need to solve X
[tex]\begin{gathered} -y^2+14y-57=4x \\ x=-\frac{1}{4}y^2+\frac{7}{2}y-\frac{57}{4} \\ \end{gathered}[/tex]we need to write the equation on this form
[tex]x=a(y-h)^2+k[/tex]where h=-(b/2a) and k=c- a (b/2a)2
we obtain a,b and c from the equation to solve x
so a=-1/4, b=7/2 and c=-57/4
now lets find h and k
[tex]\begin{gathered} h=-(\frac{b}{2a}) \\ h=-(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}}) \\ \\ h=-(\frac{\frac{7}{2}}{\frac{-1}{2}}) \\ \\ h=-(-7) \\ h=7 \end{gathered}[/tex][tex]\begin{gathered} k=c-a(\frac{b}{2a})^2 \\ \\ k=-\frac{57}{4}-(-\frac{1}{4})(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}})^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(-7)^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(49) \\ \\ k=-\frac{8}{4} \\ k=-2 \end{gathered}[/tex]now replace a, h and k on the equation
[tex]\begin{gathered} x=a(y-h)^2+k \\ \\ x=-\frac{1}{4}(y-7)^2-2 \end{gathered}[/tex]the evrtex is (h,k)=(7,-2)
