An ellipse has a center of (3, 1), a focus of (8, 1), and a directrix of x = 36.8. which is the equation of the ellipse?

The equation of the ellipse is

Step-by-step explanation:

The equation of the ellipse is given by:

where:

Center of the ellipse is (x₀,y₀)

Vertices: (x₀±a,y₀)

c: distance from the center to the focus

Eccentricity

Directrix=

So we can obtain the values:

c=(8, 1)-(3, 1)=8-3= (5,0)=5

x₀= 3

y₀= 1

The directrix is x = 36.8

Then, we have to obtain b:

The equation of the ellipse is:

the first option is correct

Step-by-step explanation: