Question 750461: this problem is confusing me..... An ellipse has a co-vertices at (4,0) and (-4,0) and foci (0,3) and (0,-3). Find the equation that can be used to describe this ellipse.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An ellipse has a co-vertices at (4,0) and (-4,0) and foci (0,3) and (0,-3). Find the equation that can be used to describe this ellipse.
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Given data shows ellipse has a vertical major axis: (y-coordinates of foci change but x-coordinates do not), but following calculations show it to be a horizontal major axis. Given data for foci should be (3,0) and (-3,0), and for co-vertices, (0,4) and (0,-4)
Its standard form of equation:  ,a>b, (h,k)=(x,y)coordinates of center.
For given ellipse:
center: (0,0)
b=4 (distance from center to co-vertices)
b^2=16
c=3 (distance from center to foci)
c^2=9
c^2=a^2-b^2
a^2=c^2+b^2=9+16=25
a=5
Equation of given ellipse:
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