+0

# the first option are A. 0.89 B. 0.45 C. 1.12

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the first option are  A. 0.89  B. 0.45  C. 1.12

the second options are A. circular then elongated or B. elongated than circular

Nov 8, 2019

#1
+109563
+1

e  =  c  /  a

c  =  √[ a^2  - b^2 ]  =   √[80 - 16]  = √64  =  8

a  =  √80  =  4√5

So

e   =    8   /  [ 4√5]   =   2 / √5    ≈  .89

If  the eccentricity  is   0.....we have a circle...so.....the closer  that the eccentricity  is to 1,  the  more elongated it is

So....this ellipse  is  more elongated than circular

See here to confirm  this, Jenny  :  https://www.desmos.com/calculator/sij3lqn4ts

Nov 8, 2019
#2
+109563
+1

As an addendum, note  when we have this

x^2        y^2

___  +  ____  =     1          ( A )

80          80

c  = √[a^2  - b^2 ]  =   √[ 80^2 - 80^2 ]  =  √0  =  0

So

c  / a    =     0  / √80  =  0

But...notice that  if  we   mutiplied    ( A)   through by   80  we get

x^2  + y^2  = 80

Which is a circle centered at the origin with a radius  of √80

So.....the closer that  e  is to   0....the more circular

And the closer that e  is to 1, the more elongated

Nov 8, 2019