Will give brainliest. +20 points

which is the equation of an ellipse with directrices at y = ±4 and foci at (0, 2) and (0, −2)?
x squared over 16 minus y squared over 4 equals 1
x squared over 4 plus y squared over 16 equals 1
x squared over 8 minus y squared over 4 equals 1
x squared over 4 plus y squared over 8 equals 1

x²/4 + y²/8 = 1

Step-by-step explanation:

Let the equa of the ellipse be : x²/a + y²/b = 1

then

F(0,c) = (0,2) ⇒ c = 2 ⇒ c² = 4

directrice  y = b²/c ⇒ b²/c = 4 ⇒ b²/2 = 4 ⇒ b² = 8

since a²=b²-c² ⇒ a²=8-4=4

finally , a²=4 and b² = 8

then x²/4 + y²/8 = 1

look at the photo below for the graph.

:)

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

not sure but it may be b, as i said i'm not sure.