Answer:
[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]
Step-by-step explanation:
The given ellipse has equation:
[tex]\frac{(y-2)^2}{64}+\frac{x^2}{9}=1[/tex].
The center of this ellipse is (h,k)=(0,2)
We use the equation: [tex]a^2-b^2=c^2[/tex] to determine the foci.
[tex]\implies 64-9=c^2[/tex]
[tex]\implies 55=c^2[/tex]
[tex]\implies c=\pm \sqrt{55}[/tex]
The directrices are given by [tex]y=k\pm\frac{a^2}{c}[/tex]
[tex]y=2\pm\frac{64}{\sqrt{55}}[/tex]
[tex]y=2\pm8.6[/tex]
[tex]y=2-8.6[/tex] and [tex]y=2+8.6[/tex]
The equation of the directrices are:
[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]
The correct answer is D
