Question

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Answer 1

Answer:

$y=-6.6$ and $y=10.6$

Step-by-step explanation:

The given ellipse has equation:

$\frac{(y-2)^2}{64}+\frac{x^2}{9}=1$.

The center of this ellipse is (h,k)=(0,2)

We use the equation: $a^2-b^2=c^2$ to determine the foci.

$\implies 64-9=c^2$

$\implies 55=c^2$

$\implies c=\pm \sqrt{55}$

The directrices are given by $y=k\pm\frac{a^2}{c}$

$y=2\pm\frac{64}{\sqrt{55}}$

$y=2\pm8.6$

$y=2-8.6$ and $y=2+8.6$

The equation of the directrices are:

$y=-6.6$ and $y=10.6$

The correct answer is D