Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0).

Step-by-step explanation:

It was given that, the ellipse has directrices at

The directrices has equation:

Where,  e is the eccentricity of the ellipse.

               >eq.1

Given the foci are (2, 0) and (−2, 0). It denotes (a e, 0) and (- a e, 0). Hence,

                a e = 2 >eq.2

Multiply eq. 1 and 2, we get

Taking square root, we get

Now substitute this ‘a’ value in eq. 2, we get

We know,

Substituting the values, we get

The equation for an ellipse is