Final answer:
The equation of the ellipse is (x-h)^2/a^2+(y-k)^2/b^2=1. The center of the ellipse is (1,4), and the lengths of the semi-major and semi-minor axes are 5 and 3 units, respectively.
Step-by-step explanation:
The equation of an ellipse in general form is (x-h)^2/a^2+(y-k)^2/b^2=1
To find the equation of the ellipse with the given vertices (-4,4),(6,4) and foci (4,4),(-2,4), we need to determine the center and the lengths of the semi-major and semi-minor axes.
By using the formula for finding the center of an ellipse, we can find that the center of the ellipse is (1,4). By observing the given vertices, we can determine that the lengths of the semi-major and semi-minor axes are 5 units and 3 units, respectively.
Therefore, the equation of the ellipse is (x-1)^2/5^2+(y-4)^2/3^2=1