What is the standard form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)?

  B) x^2/12 +y^2/16 = 1

Step-by-step explanation:

The distance from focus to covertex is the same as the distance from the center to the vertex: 4. So, the Pythagorean theorem tells you ...

  a^2 + 2^2 = b^2

  a^2 +4 = 4^2 = 16

  a^2 = 16 -4 = 12

So, the standard-form equation ...

  x^2/a^2 +y^2/b^2 = 1

looks like this when the values are filled in:

  x^2/12 +y^2/16 = 1

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32