Find the equation of the ellipse whose focus are at (0,-4) and (0,4) and are the length of its major axis is 10.

Question

Derive the equation of an ellipse given foci

Answer 1

Luckily, the Center is at the Origin.

The major axis length 2a = 10 so a = 5, and c(distance from center to either focus) = 4.

Using the fact that b² = a² - c²  we get b² = 9. 

The ellipse's equation is x²/9 + y²/25 = 1...the major axis running vertically because of the coordinate of the foci, thus 5 squared denominator is under the y squared term.