HELP WILL GIVE BRAINLIEST

Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?
(possible answers shown in image)

Step-by-step explanation:

The directrices of an ellipse are defined by

Where , and is the eccentricity defined by

So, in the first choice, we have the equation

Where and , which means and .

In an ellipse, we have the relation

Replacing values, we have

So, the eccentricity is and the directrices are , which means the first choice is not the right answer. In other words, the right answer is the second choice, because third and fourth choices don't represent an ellipse, both fractions must be positive in that case.

Therefore, the right answer is

step-by-step explanation: yes