# How do you write an equation of an ellipse in standard form with foci (0,+/- 4) and co-vertices at (+/- 4,0)?

Mar 27, 2017

The equation is ${y}^{2} / 32 + {x}^{2} / 16 = 1$

#### Explanation:

This is an ellipse with the major axis vertical.

The center is $= \left(0 , 0\right)$

The equation is

${y}^{2} / {a}^{2} + {x}^{2} / {b}^{2} = 1$

$b = 4$

$c = 4$

${a}^{2} = {b}^{2} + {c}^{2}$

$= 16 + 16 = 32$

The equation is

${y}^{2} / 32 + {x}^{2} / 16 = 1$

graph{(y^2/32+x^2/16-1)=0 [-15.55, 12.92, -8.17, 6.06]}