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An ellipse is graphed.

Which statements about the ellipse are true? Check all that apply.
The center is at (0, 0).
The major axis is 4 units long.
The vertices are 4 units to the left and right of the center.
The foci are 2sqrt3 units to the left and right of the center on the major axis.
The directrices are vertical lines.

An ellipse is graphed Which statements about the ellipse are true Check all that apply The center is at 0 0 The major axis is 4 units long The vertices are 4 un class=

Respuesta :

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?

[tex]\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}[/tex]

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

The statement third, fourth, and fifth is correct because the center is not at (0, 0), and the major axis is 8 units.

What is an ellipse?

An ellipse is an uneven oval shape created by a point moving along a plane while keeping the sum of its distances from foci constant.

As we can see the center is not at (0, 0)

The major axis is 2a where a = 4

The major axis = 2(4) = 8

The correct statements are:

3) The vertices are 4 units to the left and right of the center.

2) The foci are 2sqrt3 units to the left and right of the center on the major axis.  

3) The directrices are vertical lines.

Thus, the statement third, fourth, and fifth is correct because the center is not at (0, 0), and the major axis is 8 units.

Learn more about the ellipse here:

https://brainly.com/question/19507943

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