Final answer:
To find the equation of the ellipse, we can use the given coordinates and the formula for the equation of an ellipse.
Step-by-step explanation:
In this question, we are given the coordinates (3,2) as one endpoint of the transverse axis, and the coordinates (-1,2) as one focus. We need to determine the equation of the ellipse.
Step 1: Determine the center of the ellipse by finding the midpoint of the transverse axis. The midpoint is ((3 + 7)/2, (2 + 2)/2), which simplifies to (5, 2).
Step 2: Determine the distance between the center and the focus. The distance is |(-1) - 5| = 6.
Step 3: Determine the length of the transverse axis. The length is |3 - 7| = 4.
Step 4: Use the formula for the equation of an ellipse centered at (h, k) with the major axis along the x-axis, a transverse axis length of 2a, and a focal length of 2c: (x - h)^2/a^2 + (y - k)^2/b^2 = 1. Plugging in the values we found, we get the equation (x - 5)^2/2^2 + (y - 2)^2/3^2 = 1.