Answer:
B) (-5, 1) and (-5, -7)
F) (-1, -3) and (-9, -3)
Step-by-step explanation:
The major axis of an ellipse is the longest diameter that passes through its center and both foci, extending to the vertices at either end.
The center of the ellipse is also the center point of the major axis. Therefore, if the major axis of an ellipse is 8 units long, the vertices will be either 4 units to the left and right of the center on a line parallel to the horizontal axis, or 4 units above and below the center on a line parallel to the vertical axis.
Given that the center is located at (-5, -3), to find the pairs of coordinates that could represent the vertices of the graph of the ellipse, we:
- Add and subtract 4 from the y-coordinate while keeping the x-coordinate the same.
- Add and subtract 4 from the x-coordinate while keeping the y-coordinate the same.
Therefore:
(-5, -3 + 4) and (-5, -3 - 4) = (-5, 1) and (-5, -7)
(-5 + 4, -3) and (-5 - 4, -3) = (-1, -3) and (-9, -3)
So, the pairs of coordinates that could represent the vertices of the graph of the ellipse are:
[tex]\Large\boxed{(-5, 1) \;\textsf{and}\; (-5, -7)}[/tex]
[tex]\Large\boxed{(-1, -3) \;\textsf{and}\; (-9, -3)}[/tex]
