Question 630207: Find the equation in standard form of the ellipse, given the information provided.
Vertices (6, 12) and (6, −4), foci at (6, 8) and (6, 0)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equation in standard form of the ellipse, given the information provided.
Vertices (6, 12) and (6, −4), foci at (6, 8) and (6, 0)
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Given info shows that ellipse has a vertical major axis
Its standard form of equation:  , a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
center:(6,4)
length of vertical major axis=16 (-4 to 12)=2a
a=8
a^2=64
..
foci:
c=4 (0 to 8)/2
c^2=16
..
c^2=a^2-b^2
b^2=a^2-c^2=64-16=48
Equation of given ellipse:
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