Question

Identify the focus and directrix of the parabola given by y^2 + 5x=0

Answer 1

\(\bf y^2 + 5x=0\implies y^2=-5x\implies (y-{\color{purple}{ 0}})^2=-5(x-{\color{purple}{ 0}})
\\ \quad \\
\textit{keep in mind }(y-{\color{purple}{ k}})^2=4{\color{blue}{ p}}(x-{\color{purple}{ h}})\quad vertex\ ({\color{purple}{ h,k}})
\\ \quad \\
{\color{blue}{ p}}=\textit{distance from the vertex to the focus and directrix}\)

Answer 2

so just find "p" distance, and move that many units, from the vertex to one side, to get the focus, and to the other side, to get the directrix

notice the "y" is squared, thus is horizontal parabola