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The ellipse x^2/49+y^2/b^2=1 has foci at (5,0) and (-5,0).
(a) Fimd the length of a semi major axis of this ellipse
(b)compute the value of b

 Feb 17, 2021
 #1
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x^2/49   +  y^2 / b^2    =    1

 

The   center is  (0, 0)

 

c   =  distance  from  the  center  to either focal point  =  5

a  = sqrt (49)   = 7  =  length of semi-major axis

 

b  =  sqrt (a^2   - c^2 )   =   sqrt ( 7^2   - 5^2 )   = sqrt ( 49  -  25 )  =  sqrt  (24)   =  2sqrt (6)

 

Equation is

 

x^2/49   + y^2/24     = 1

 

See the graph  here  :  https://www.desmos.com/calculator/3l1f0moddl

 

 

cool cool cool

 Feb 17, 2021

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