Equation:
[tex](y+1)^2=6(x-5)[/tex]
The vertex is given by the following formula:
[tex](y-k)^2=4p(x-h)[/tex]
where the vertex is (h, k). Thus, in our equation k = -1 and h = 5, and the vertex
is (5, -1).
Additionally, the focus is given by (h+p, k). In our case:
[tex]p=\frac{6}{4}=\frac{3}{2}[/tex]
Then, the focus is:
[tex](5+\frac{3}{2},-1)[/tex]
Simplifying:
[tex](\frac{13}{2},-1)[/tex]
The directrix is x = h - p:
[tex]x=5-\frac{3}{2}=\frac{7}{2}[/tex]
Finally, the axis of symmetry is y = -1.
