The focus of a parabola is given by:
[tex]F(h,k+p)[/tex]and the directrix is given by:
[tex]y=k-p[/tex]since the directrix is x = 9, we can conclude it is a horizontal parabola, so:
[tex]\begin{gathered} x=9=k-p \\ so\colon \\ k=9+p \end{gathered}[/tex][tex]\begin{gathered} F(-7,3)=(h,k+p) \\ h=-7 \\ k+p=3 \\ 9+p+p=3 \\ 9+2p=3 \end{gathered}[/tex]solve for p:
[tex]\begin{gathered} 2p=3-9 \\ 2p=-6 \\ p=-\frac{6}{2} \\ p=-3 \end{gathered}[/tex][tex]\begin{gathered} k=3-p \\ k=3-(-3) \\ k=6 \end{gathered}[/tex]We can write the parabola in its vertex form:
[tex]\begin{gathered} x=\frac{1}{4p}(y-k)^2+h \\ so\colon \\ x=-\frac{1}{12}(y-6)^2-7 \end{gathered}[/tex]It is a horizontal parabola that opens to the left, and has vertex located at (-7,6)
