Question

find the vertex focus and directrix of the parabola.
y^2-6y+8x+9=0

The vertex of the parabola is___ (write order pair)

The focus is _____ (write order pair)

what is the directrix? select the correct choice below.
y=__________
OR
x=__________

Answer 1

Where is @directrix lol.

Answer 2

Complete the square.$$\begin{align*}y^2-6y+8x+9&=y^2-6y+9+8x\\&=(y-3)^2+8x\end{align*}$$Since we have \((y-3)^2+8x=0\) we may rearrange to yield
\(-8x=(y-3)^2\). This means our directrix and focus are \(-8/4=-2\) away from the vertex \((0,3)\); since this is a left-opening horizontal parabola (hence the \(-\) and \(y^2\)), meaning our focus is at \((-2,3)\) and our directrix \(x=2\).