Question

An ellipse is graphed.

Answer 1

• The vertices are 4 units to the left and right of the center.
• The f-o-c-i are 2√3 units to the left and right of the center on the major axis.
• The direct rices are vertical lines.

It was 3,4,5 on edge.

Answer 2

Well, notice the graph, the center is clearly not at the origin.

well, the major axis is horizontal, notice the distance from the center to a vertex, is 4 units, and the major axis is 2a, namely 2(4).

the foci are the points at "c" distance from the center of the ellipse over the major axis, hmmmm what is "c" anyway?

$\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2}\\ \end{cases} \\\\ -------------------------------\\\\ \begin{cases} a=4\\ b=2 \end{cases}\implies c=\sqrt{4^2-2^2}\implies c=\sqrt{12}\implies c=\sqrt{4\cdot 3} \\\\\\ c=\sqrt{2^2\cdot 3}\implies c=2\sqrt{3}$

the directrices are lines parallel with the minor axis, and away from the vertices, in this case they're be two vertical lines.