Question

Given the ellipse worth foci at (5,3) and (5,-5) and a major axis of length 12,determine the center using ( , ) and the denominators of the equation.

Answer 1

Major axis = 12, thus a = 6
Length between foci = 8, thus c = 4
a^2 = b^2 + c^2
36 = b^2 + 16
--> b^2 = 20

ok since c = 4 and 3-4 = -1
center is at (5,-1)
Equation:
\[\frac{(x-5)^{2}}{36} + \frac{(y+1)^{2}}{20} = 1\]

Answer 2

oops i got it mixed up...the 36 should be under the y, and the 20 under the x
sorry