Question

What is the directrix of a parabola whose equation is (y + 3)2 = 8(x − 3)?

Answer 1

\(\large {
\begin{array}{llll}
(y-{\color{blue}{ k}})^2=4{\color{purple}{ p}}(x-{\color{brown}{ h}}) \\

\end{array}

\qquad
\begin{array}{llll}
vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\
{\color{purple}{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}
\\ \quad \\
(y + 3)^2 = 8(x - 3)
}\)

any ideas on the vertex coordinates?

what about theh "p" distance?

Answer 2

The directrix of a parabola y^2=4px is x=-p
Translating by the vertex by (3,-3), the parabola becomes 8(x-3)=(y+3)^2
from which we can equate 4p=8, or p=2 units to the left of the vertex, which means that the directrix is at x=3-2=1.