vertex: (5,4) focus (-5,4)

Since the y coordinates of the vertex and the focus are the same, the focus and the vertex are on the same horizontal line, y=4. So,the axis of symmetry is a horizontal line.

SInce vertex: (5,4) and focus (-5,4), we find that the focus is at the left of the vertex. So, the parabola opens leftwards.

So, the equation of parabola is,

[tex]\begin{gathered} (y-k)^2=4a(x-h) \\ \text{Here, vertex(}h,k)=(5,4) \end{gathered}[/tex]

a=-5-(5)=-10 , since y coordinates are same.

Now, above equation becomes,

[tex]\begin{gathered} (y-4)^2=4\times(-10)(x-5) \\ (y-4)^2=-40(x-5) \end{gathered}[/tex]

So, the equation of the parabola is,

[tex]\begin{gathered} \\ (y-4)^2=-40(x-5) \end{gathered}[/tex]