Answer:[tex](x-5)^2=-20(y-4)[/tex]
Step-by-step explanation:
Given
Vertex of parabola is [tex](5,4)[/tex]
and directrix is [tex]y=9[/tex]
as directrix is above vertex so it downward facing parabola
Distance between directrix and parabola is
[tex]\mid 9-4\mid=5[/tex]
so value of [tex]a=5[/tex]
Equation of parabola is
[tex](x-5)^2=-4a(y-4)[/tex]
[tex](x-5)^2=-4(5)(y-4)[/tex]
[tex](x-5)^2=-20(y-4)[/tex]
