SOLUTION: equation of ellipse with the center (2,-3) foci at (2,-7) and (2,1) and a minor axis 12 units long

Question 520209: equation of ellipse with the center (2,-3) foci at (2,-7) and (2,1) and a minor axis 12 units long
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
equation of ellipse with the center (2,-3) foci at (2,-7) and (2,1) and a minor axis 12 units long
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Given equation is that of an ellipse with vertical major axis of the standard form:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k) being the (x,y) coordinates of the center
For given equation:
Center: (2,-3)
length of minor axis=2b=12
b=6
b^2=36
c=4 ( from foci coordinates)
c^2=16
c^2=a^2-b^2
a^2=c^2+b^2=16+36=52
a=√52≈7.21
Equation of given ellipse:
(x-2)^2/36+(y+3)^2/52=1
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