Write the equation of the ellipse with foci at (0, ±24) and minor axis length 14.
The major axis is vertical and passes through the foci, so the center of the ellipse is at (0,0). We know that c=24 and b=7 (half of the minor axis length). To find a (half of the major axis length), we can use the formula c² = a² - b²:
24² = a² - 7²
a² = 24² + 7²
a² = 625
a = 25
So the equation of the ellipse is:
(x/25)² + (y/7)² = 1