SOLUTION: What is the equation of ellipse whose vertices are (5,0) and (-5,0) and length of latus rectum is 8/5? Thanks!

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Question 933264: What is the equation of ellipse whose vertices are (5,0) and (-5,0) and length of latus rectum is 8/5? Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
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the equation of ellipse whose vertices are (5,0) and (-5,0) and length of latus rectum is 8%2F5:
standard form of equation:
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1, ....a%3Eb
vertices:(0±a,0)=(5,0) => a=5 and a=-5
The Latus Rectum is the line through the focus and parallel to the directrix.
The length of the Latus Rectum is 2b%5E2%2Fa
since latus rectum is 8%2F5 and a=5, we have
2b%5E2%2F5=+8%2F5 now find b,..denominators same then
2b%5E2=+8
b%5E2=+4
b=2 or b=-2
x%5E2%2F5%5E2%2By%5E2%2F2%5E2=1
x%5E2%2F25%2By%5E2%2F4=1