An ellipse has a Center C = (0,0) and foci are located at (0,8) and (0,-8). The length of the major axis is 24. Fill in the missing denominators for the equation of the ellipse.
x^2 + y^2 = 1
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The foci have different y-coordinates which indicates that the foci lie in the y axis. Therefore, the major axis is the y axis. The equation of the ellipse has the form
`(x-h)^2/b^2+(y-k)^2/a^2=1` where center is (h, k) and a ≥ b > 0.
For a vertical ellipse, foci are (h, k±c) where c is the focal distance given by `sqrt(a^2-b^2)` .
Here, center =(0,0). So, from the coordinates of the foci, c=8.
From the length of the major axis, we obtain a=24/2=12. Hence
Also, `b^2=a^2-c^2` =144-64=80
Now plugging in the values of `a^2` and `b^2` to the equation we get:
Therefore, the required equation of the ellipse is `x^2/80+y^2/144=1.`
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