Write an equation for an ellipse centered at the origin, which has foci at (\pm\sqrt{8},0)(± 8 ,0)(, plus minus, square root of, 8, end square root, comma, 0, )and co-vertices at (0,\pm\sqrt{10})(0,± 10 )(, 0, comma, plus minus, square root of, 10, end square root, ).

The equation of ellipse centered at the origin

Step-by-step explanation:

given the foci of ellipse (±√8,0) and c0-vertices are (0,±√10)

The foci are (-C,0) and (C ,0)

Given data (±√8,0)  

the focus has x-coordinates so the focus is  lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so c0-vertices are (0,±√10)

given focus C = ae = √8

Given co-vertices ( minor axis) (0,±b) = (0,±√10)

b= √10

The relation between the focus and semi major axes and semi minor axes are

The equation of ellipse formula

we know that

Final -

The equation of ellipse centered at the origin