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Find the eccentricity of the ellipse:2x 2 +4y 2 =4.what is the eccentricity

Find the eccentricity of the ellipse:2x2+4y2=4.what is the eccentricity
 

Grade:10

1 Answers

Ram Kushwah
110 Points
6 months ago
The bequation of ellipse is
2x²+4y²=4
Or x²/2+y²/1=1
so since the denominator of x²/2 is graeter then denominator of y²/1
Thus major axis is along x-axis
Comparing the given equation with the standard equation
x²/a²+y²/b²=1
We have so a=√2 and b=1
so c=√(a²-b²)
=√(2-1) =1
so c=1
Thus the eccentricity of the ellipse:
e=c/a=1/√2
What is eccentricity?
The eccentricity of an ellipse is the ratio of the distances from the centre
of the ellipse to the distance of a foci from the centre of ellipse
   The eccentricity of an ellipse is measure of that how nearly circular is the ellipse.
The example in the following figure will clear the meaning of ecentricity of a ellipse.

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