Write an equation of the ellipse with foci at (±3, 0) and co-vertices at (0, ±1)
To find the equation of the ellipse, we need to determine the length of the major and minor axes, as well as the coordinates of the center. The center of the ellipse is the midpoint between the foci, which is (0,0).
The distance between the foci is given by 2a, where a is the length of the semi-major axis. In this case, 2a = 6, so a = 3.
The distance between the center and the co-vertices is given by 2b, where b is the length of the semi-minor axis. In this case, 2b = 2, so b = 1.
Therefore, the equation of the ellipse with foci at (±3, 0) and co-vertices at (0, ±1) is:
(x^2/3^2) + (y^2/1^2) = 1