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Let O be the center and let F be one of the foci of the ellipse 25x^2 +16 y^2 = 400. A second ellipse, lying inside and tangent to the first ellipse, has its foci at O and F.  Where is the center of the second ellipse?

 Jun 3, 2021
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25x^2  + 16y^2    =  400         divide through  by    400

 

x^2             y^2

____   +    ____   =      1

 16              25

 

 

The center  is   (0,0)........the  foci  lies on the  y  axis  .....so   let F  =  (0, sqrt (25 - 16)  = (0, sqrt (9) )  =

 

(0, 3 )  = F

 

The  center of the  second ellipse  is the  the  midpoint of  O   and F   =   (0,0)  and (0,3)  =   (0, 3/2)

 

 

cool cool cool

 Jun 3, 2021

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