Answer:
The required equation is [tex](x+4)^2=-36(y+6)[/tex].
Step-by-step explanation:
The standard form of the equation of the parabola is
[tex](x-h)^2=4p(y-k)[/tex] .... (1)
where, (h, k) is vertex and y = k - p is directrix.
It is given that vertex of parabola is (–4, –6) and the directrix is y = 3.
[tex](-4,-6)=(h,k)[/tex]
On comparing both the sides, we get
[tex]h=-4,k=-6[/tex]
Directrix of the parabola is
[tex]y=k-p[/tex]
Put y=3 and k=-6 in the above equation.
[tex]3=-6-p[/tex]
[tex]3+6=-p[/tex]
[tex]9=-p[/tex]
[tex]-9=p[/tex]
Substitute h=-4,p=-9 and k=-6 in equation (1).
[tex](x-(-4))^2=4(-9)(y-(-6))[/tex]
[tex](x+4)^2=-36(y+6)[/tex]
Therefore the required equation is [tex](x+4)^2=-36(y+6)[/tex].
