SOLUTION: The foci of a ellipse are F1(2,0) and F2(-2,0) and the sum of the focal radii is 6 units. Find the equation. Thanks so much in advance:)

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Question 818004: The foci of a ellipse are F1(2,0) and F2(-2,0) and the sum of the focal radii is 6 units. Find the equation.
Thanks so much in advance:)
Found 2 solutions by lwsshak3, TimothyLamb:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
The foci of a ellipse are F1(2,0) and F2(-2,0) and the sum of the focal radii is 6 units. Find the equation.
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Given ellipse has a horizontal major axis with center at the origin.
Its standard form of equation:
center:(0,0)
sum of the focal radii=6=2a
a=3
a^2=9
c=2
c^2=4
c^2=a^2-b^2
b^2=a^2-c^2=9-4=5
Equation of given ellipse:

Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website!
eccentricity:
f^2 = a^2 − b^2
f = 2
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sum of focal radii is 6:
2a = 6
a = 3
---
f^2 = a^2 − b^2
2^2 = 3^2 − b^2
4 = 9 − b^2
b^2 = 5
b = sqrt( 5 )
b = 2.236068
---
ellipse eqn:
(x/a)^2 + (y/a)^2 = 1
(x/3)^2 + (y/sqrt( 5 ))^2 = 1
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answer:
(1/9)x^2 + (1/5)y^2 = 1
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