SOLUTION: center at (6,5); focus at (11,5); ellipse passes through the point (6,8)

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Question 734557: center at (6,5); focus at (11,5); ellipse passes through the point (6,8)
Answer by lwsshak3(11628) About Me  (Show Source):
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center at (6,5); focus at (11,5); ellipse passes through the point (6,8)
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Give data shows that ellipse has a horizontal major axis.
Its standard form of equation:%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center.
For given problem:
%28x-6%29%5E2%2Fa%5E2%2B%28y-5%29%5E2%2Fb%5E2=1
plug in given point(6,8)on the ellipse
%286-6%29%5E2%2Fa%5E2%2B%288-5%29%5E2%2Fb%5E2=1
0%2B%283%29%5E2%2Fb%5E2=1
9=b%5E2
b=3
c=5 (distance from center to focus (6 to 11))
c^2=25=a^2-b^2
a^2=c^2+b^2=25+9=34
Equation of given ellipse:
%28x-6%29%5E2%2F34%2B%28y-5%29%5E2%2F9=1