Which is equation of an ellipse of an ellipse with directrices at x=4 and foci at (2,0) (-2,0)

Step-by-step explanation:

The directrices in this case are vertical lines, so we have a horizontal ellipse. The equation for that ellipse is:

The center of the ellipse is (h,k), the diretrix is x = d and the foci are given by (h+c, k) and (h-c, k)

So, comparing the foci, we have that k = 0 and:

Adding these two equations, we have:

We can find the value of a^2 using the property:

Using c = 2 and d = 4, we have:

Now, to find b^2, we use the property:

So the equation of the ellipse is:

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.