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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oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

`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)  

            

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

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.

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