# The eccentricity of an ellipse is a measure of how nearly circular it is. Eccentricity is defined as c/a, where c is the distance from the center to a focus and a is the distance from the center to...

The eccentricity of an ellipse is a measure of how nearly circular it is. Eccentricity is defined as c/a, where c is the distance from the center to a focus and a is the distance from the center to a vertex.

a. Find the eccentricity of an ellipse with foci (±9,0) and vertices (±10,0). Sketch the graph.

b. Describe the shape of an ellipse that has an eccentricity close to 0.

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### 3 Answers

`a)` set: `b^2=a^2-c^2` so equationis is:

`x^2/10^2 +y^2/(10^2-9^2)=1` `x^2/100+y^2/19=1`

`e= 0.9`

`b)` `x^2/100-y^2/99=1` `e=0.1`

`c)` The ellipse in `b)` has eccentricity close to 0 and looks

and pushed on the y ass,.

`d) ` The ellipse in `a)` has eccentricity close to 1, and looks

like a cirlce ( indeed in a cirlce the ecentricity (r/r) is

equal to 1)

Sorry I slipped b^2=100xx.19=19

an shape of ellipse is not proper.

Let equation of the ellipse be `x^2/a^2+y^2/b^2=1 ,where`

`b^2=a^2(1-e^2)` ,its foci are `(+-ae,0)` and vertices are `(+-a,0),(0,+-b)` .Its centre is (0,0).

Given

ae=9 and a=10

e=9/10

e=.9

Thus `b^2=10xx(.19)=19`

thus equation of the ellipse is

`x^2/100+y^2/19=1`

When eccentricity close to zero.

Almost it will looks like a circle.