Question

Which statements about the ellipse are true? Select three options.

Answer 1

Answer:

The 1st, 3rd and the 4th statements are true.

Step-by-step explanation:

The center of an ellipse may be at any point on the coordinate plane.

So, 'The center is at (-4,2)' statement is true.

If the distance from center to each covertex can not be the same because an ellipse has major and minor axes.

So, 'The distance between the center and each covertex is 3  units' statement is not true.

The two vertices may be at any two points.

So, 'The vertices are at (-7, 1) and (-1, 1)' statement is also true.

The two focuses are at equal distance from the center.

So, 'Each focus is approximately 2.65 units above or below the center' statement is also true.

The directrices are not always horizontal.

So, 'The directrices are horizontal lines approximately 6 units  from the center on the major axis' statement is also not true.

Therefore, the 1st, 3rd, and 4th statements are true. (Answer)

Answer 2

Answer:

The center is at (-4,2).

The vertices are at (-7, 1) and (-1, 1).

Each focus is approximately 2.65 units above or below  the center.

Step-by-step explanation:

The statement 'The center is at (-4,2)' is true as any point on the coordinate plane can be the centre.

The statement 'The distance between the center and each covertex is 3  units' statement is not true as the distance from center to each covertex can not be the same since an ellipse has both major and minor axes.

The statement 'The vertices are at (-7, 1) and (-1, 1)' statement is true as any two points on the coordinate plane can be the vertices.

The statement 'Each focus is approximately 2.65 units above or below the center' statement is true as the two focuses are always at equal distance from the center.

The statement 'The directrices are horizontal lines approximately 6 units  from the center on the major axis' statement is not true as the directrices