The ellipse is 5 meters across and 8 meters long with decorative fountains located at the foci. How far from the center should the fountains be located? (Rounded to the nearest hundredth). How far apart are the fountains?
I feel like this problem is a lot easier than what I'm making it.
Answer:
$$2a = 8 => a = 4$$
$$2b = 5 => b = 5/2$$
$$c = \sqrt{a^{2}-b^{2}}$$
Part I :The distance from the center to the focus:$$c = \sqrt{39}/2$$
Part II: The fountains are 2*c apart from each other$$2c = \sqrt{39}$$