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Question 631611: Graph the ellipse. Specify the lengths of the major and minor axes, the foci, and the eccentricity?
2x^2+3y^2=3
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Graph the ellipse. Specify the lengths of the major and minor axes, the foci, and the eccentricity?
2x^2+3y^2=3
divide by 3
x^2/(3/2)+y^2/1=1
This is an equation of an ellipse with horizontal major axis
Its standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), (h,k)=(x,y) coordinates of center.
For given equation:
center: (0,0)
a^2=(3/2)
a=√(3/2)
length of major axis=2a=2√(3/2)≈2.5
..
b^2=1
b=1
length of minor axis=2b=2
..
Foci:
c^2=a^2-b^2=(3/2)-1=0.5
c=√0.5≈.71 (distance from center to focus)
..
eccentricity=c/a≈√.5/√(3/2)=√(1/3)≈.58
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