The basic formula for an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1; where (h,k) is the center of the ellipse and a is the distance from the center to each "x" vertex and "b" is the distance from the center to the "y" vertex.
In the first, the center is (0,0) because that is the half way point between the verticies. The major axis has a length of 8, that means that the value of "a" is half of 8 or 4 (a=4). b=3
That gives us: x^2/16 + y^2/9 =1
The second, also has a center at (0,0). This time a=5 and b=2.