Question

An ellipse is represented by the equation .

Each directrix of this ellipse is a from the center on the major axis.

Answer 1

Answer:

31.25 units from the center on the major axis

Step-by-step explanation:

From the equation of the ellipse we can see that

• $a^2=625\Rightarrow a=25;$
• $b^2=225\Rightarrow b=15;$
• the center of the ellipse has coordinates (5,4).

If a=25, b=15, then

$c^2=a^2-b^2,\\ \\c^2=625-225,\\ \\c^2=400,\\ \\c=20.$

Then

$e=\dfrac{c}{a}=\dfrac{20}{25}=0.8.$

The directrices have equations

$x-x_0=\pm \dfrac{a}{e},\\ \\x-5=\pm \dfrac{25}{0.8},\\ \\x=5\pm 31.25,\\ \\x=36.25 \text{ or } x=-26.25$

and are 31.25 units from the center on the major axis.

Answer 2

Answer:

D aka vertical line that is 31.25 units

Step-by-step explanation:

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