SOLUTION: Find an equation of the ellipse having a major axis of length 8 and Foci at (1,2) and (-3,2)

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Question 1180755: Find an equation of the ellipse having a major axis of length 8 and Foci at (1,2) and (-3,2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
an equation of the ellipse:
%28x-h%29%2Fa%5E2%2B%28y-k%29%2Fb%5E2=1

a major axis of length 8: =>2a=8=>a=4

Foci at (1,2) and (-3,2)=> center is half way between
(h,k)=(1%2B%28-3%29%29%2F2,2)=(-1,2)
center: (h,k)=(-1,2)
-> since c is the distance from the focus to center
c=2
b=sqrt%28a%5E2-c%5E2%29
b=sqrt%284%5E2-2%5E2%29
b=sqrt%2816-4%29
b=sqrt%2812%29

%28x-%28-1%29%29%5E2%2F4%5E2%2B%28y-2%29%5E2%2F%28sqrt%2812%29%29%5E2=1
%28x%2B1%29%5E2%2F16%2B%28y-2%29%5E2%2F12=1