Final answer:
To determine the equation of the ellipse with a vertical major axis, we need to find the length of the major axis and the semimajor axis. The length of the major axis can be found using the distance formula, and the semimajor axis is half the length of the major axis. The equation of the ellipse is x^2/5 + y^2/b^2 = 1.
Step-by-step explanation:
To determine the equation of the ellipse, we can use the general equation of an ellipse with the major axis as vertical. The general equation is given by x^2/a^2 + y^2/b^2 = 1, where a represents the semimajor axis and b represents the semiminor axis. Since the major axis is vertical, the semimajor axis is equal to the length of the major axis, which is the distance between the two given points on the ellipse, (0, 4) and (2, 0).
Using the distance formula, we can find the length of the major axis:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((2 - 0)^2 + (0 - 4)^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)
Since the semimajor axis is half the length of the major axis, we have a = sqrt(5).
Therefore, the equation of the ellipse is:
x^2/5 + y^2/b^2 = 1