Question

Find the standard form of the equation of the ellipse with the given characteristics.
center: (- 4, 7)
a = 4c
foci: (- 5, 7), (- 3, 7)

I know what to do with the center but i dont know what to do with 'a'

Answer 1

Well, c is the distance from the center to the foci. SO in this case c is just 1. So that means that a = 4. Now that you have a and c, you can find b. b^2 = a^2 - c^2, so b^2 = 16-1 = 15. So we have all of our a b and c values now. Because in this problem it is y value that is constant, this tells us that our a^2 will go under the (x-h)^2 term. Using our center, we can find the (x-h)^2 and (y-k)^2 terms. So (x-h)^2 = (x-(-4))^2 = (x+4)^2. Then (y-k)^2 = (y-7)^2. So the full answer is (x+4)^2/16 + (y-7)^2/15 = 1