Write an equation for the following: a) The ellipse has foci (2, 0) and (–2, 0) and vertices (4, 0) and (–4, 0). b) The ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal.

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:

positive

step-by-step explanation:

the quadrant is facing upwards