Write an equation of the ellipse with foci at (0, ±11) and vertices at (0, ±12).
The center of the ellipse is at (0,0) as it is the midpoint of the line connecting the foci. Also, the distance between the foci is 2c = 11+11 = 22. The distance between the vertices is 2a = 12+12 = 24. The equation of the ellipse is:
(x^2/a^2) + (y^2/b^2) = 1
where a = 12 and c = 11.
To find b, we use the relationship:
b^2 = a^2 - c^2
b^2 = 12^2 - 11^2 = 23
Therefore, the equation of the ellipse is:
(x^2/144) + (y^2/23) = 1.