SOLUTION: find the equation of the conic given: foci:(0,8) (0,-8) and vertices (0,11)(0,-11)

Question 384959: find the equation of the conic given: foci:(0,8) (0,-8) and vertices (0,11)(0,-11)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the equation of the conic given: foci:(0,8) (0,-8) and vertices (0,11)(0,-11)
what conic is this? Its not a circle, because circles do not have foci and vertices.
Parabolas have foci and vertices but only one of each
Hyperbolas have foci and vertices but the foci is greater in length than the vertices.
Only one other conic remains and that is the ellipse which fits the given data.
Standard equation of an ellipse: (x-h)^2/a^2+(y-k)^2/b^2 = 1, a>b (major axis horizontal)
(y-k)^2/a^2+(x-h)^2/b^2 = 1, a>b (major axis vertical)
(h,k) being the (x,y) coordinates of the center of the ellipse
given: c=8
c^2=64
a=11
a^2=121
c^2=a^2-b^2
b^2=a^2-c^2=121-64=57
now that we have a^2 and b^2, we must find the center (h,k)
from the given data it can be seen that h=0, and k=0
equation of the ellipse is:(y-0)^2/a^2+(x-0)^2/b^2=1
or y^2/121 + x^2/57 =1
see the graph below:

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