Question 671937: The major axis of an ellipse is 12 units and the foci are at (-4,-1)and (-4,7).Find the standard form of the equation of this ellipse,the length of minor axis ,the vertices and coordinates where the ellipse intercepts the minor axis.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The major axis of an ellipse is 12 units and the foci are at (-4,-1)and (-4,7).Find the standard form of the equation of this ellipse,the length of minor axis ,the vertices and coordinates where the ellipse intercepts the minor axis.
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This is an ellipse with vertical major axis.
Its standard form of equation:  , a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
From given coordinates of foci
center: (-4,3)
given length of vertical major axis=12=2a
a=6
a^2=36
vertices: (-4,3±a)=(-4,3±6)=(-4,-3) and (-4,9)
c=4 (distance from center to foci)
c^2=16
c^2=a^2-b^2
b^2=a^2-c^2=36-16=20
b=√20≈4.47
length of minor axis=2b=2√20
where ellipse intercepts minor axis: (-4±b,3)=(-4±√20,3)=(-4-√20,3) and (-4+√20,3)
equation of given ellipse:
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