Final Answer:
The distance from point A(3, a) to point B(3, b) on the given ellipse is 3 coordinate units.
Step-by-step explanation:
To find the distance between points A and B on the ellipse, we can use the distance formula:
. In this case, the x-coordinates of A and B are both 3, and their y-coordinates are a and b, respectively.
The general equation of an ellipse centered at the origin is given by
, where a and b are the semi-major and semi-minor axes, respectively. Since the ellipse is centered at (0, 0) and passes through points (-5, 0), (0, 3), (5, 0), and (0, -3), we can deduce that the semi-major axis
is 5, and the semi-minor axis
is 3.
Now, plug the coordinates of points A and B into the distance formula:
For point A(3, a):

For point B(3, b):

Since both points have the same x-coordinate (3), the distance between them is simply the absolute difference of their y-coordinates, which is
. Given that the ellipse passes through (0, 3) and (0, -3), we know

Therefore, the distance from A to B on the ellipse is 3 coordinate units.