Final answer:
To find the equation for the semi-ellipse, we need to determine the coordinates of the foci. The standard form equation for an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h, k) are the coordinates of the center, and a and b are the semi-axes along the x and y directions, respectively.
Step-by-step explanation:
An ellipse is a closed curve, and the sum of the distances from any point on the curve to the two foci is always constant. The arch in question is a semi-ellipse, meaning it is half of an ellipse. To find the equation for the ellipse, we need to determine the coordinates of the foci.
Step 1: Find the coordinates of the center of the ellipse. The center is the midpoint of the span, so its x-coordinate is 0 and its y-coordinate is half the height, which is 6 feet.
Step 2: Find the distance from the center to each focus. The distance from the center to each focus is half the span, so it is 20 feet.
Step 3: Write the equation for the ellipse. The standard form equation for an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h, k) are the coordinates of the center, and a and b are the semi-axes along the x and y directions, respectively. For the given ellipse, the equation is (x-0)^2/20^2 + (y-6)^2/b^2 = 1.