SOLUTION: find the standard form of the equation of the specified ellipse Foci: (5,5), (1,5) Major axis of length 10

Question 539097: find the standard form of the equation of the specified ellipse
Foci: (5,5), (1,5)
Major axis of length 10
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the standard form of the equation of the specified ellipse
Foci: (5,5), (1,5)
Major axis of length 10.
**
Data given shows this is an ellipse with horizontal major axis with equation of the standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, with (h,k) being the coordinates of the center.
..
y-coordinate of center=5
x-coordinate of center=(5+1)/2=3
center: (3,5)
..
length of horizontal major axis=10=2a
a=5
a^2=25
..
c=2 (distance from center to focus on major axis)
c^2=4
c^2=a^2-b^2
b^2=a^2-c^2=25-4=21
..
Equation:
(x-3)/25+(y-5)^2/21=1
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