Answer:
a)
b)
Step-by-step explanation:
a)
The vertices are located in the x-axis, so we have a horizontal ellipse.
The equation of an ellipse is given by:
The coordinates of the foci and the vertices are given by:
Foci:
Vertices:
Comparing the coordinates with the values given, we have that:
h = 0, k = 0, c = 2, a = 4
To find the value of b we can use the following equation:
So the equation of the ellipse is:
b)
If the ellipse is centered at the origin, we have:
h = 0, k = 0
The major axis is 'a' and the other axis is 'b', so we have:
a = 8, b = 4.
So the equation is: