Write an equation for an ellipse centered at the origin, which has foci at (0,\pm\sqrt{63})(0,± 63 )left parenthesis, 0, comma, plus minus, square root of, 63, end square root, right parenthesis and vertices at (0,\pm\sqrt{91})(0,± 91 )left parenthesis, 0, comma, plus minus, square root of, 91, end square root, right parenthesis.

Step-by-step explanation:

Since the foci are at(0,±c) = (0,±63) and vertices (0,±a) = (0,±91), the major axis is the y- axis. So, we have the equation in the form (with center at the origin) .

We find the co-vertices b from b = ±√(a² - c²) where a = 91 and c = 63

b = ±√(a² - c²)

= ±√(91² - 63²)

= ±√(8281 - 3969)

= ±√4312

= ±14√22

So the equation is