Final answer:
The equation of the ellipse with given foci and minor axis
Step-by-step explanation:
The equation of an ellipse with foci at (h,k) and (h,-k) and a minor axis of length 2b is:
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
In this case, the foci are at (2, 4) and (2, -4), and the minor axis has a length of 6. Therefore, the value of 2b is 6, which means b = 3.
Since the foci are at the same x-coordinate, the value of h is 2. So, the equation of the ellipse is:
((x-2)^2)/(a^2) + ((y-k)^2)/(9) = 1