SOLUTION: An ellipse has center ( 0,0) and one vertex a(10,0) . Find the equation of the ellipse if it passes through r(6,4). Thanks so much in advance

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: An ellipse has center ( 0,0) and one vertex a(10,0) . Find the equation of the ellipse if it passes through r(6,4). Thanks so much in advance      Log On


   

Question 818442: An ellipse has center ( 0,0) and one vertex a(10,0) . Find the equation of the ellipse if it passes through r(6,4).
Thanks so much in advance
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
An ellipse has center ( 0,0) and one vertex a(10,0) . Find the equation of the ellipse if it passes through r(6,4).
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Given ellipse has a horizontal major axis and center at the origin.
Its standard form of equation: x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1, a>b
..
a=10(distance from center to vertices)
a^2=100
equation:6%5E2%2F100%2B4%5E2%2Fb%5E2=1
solving for b^2
36%2F100%2B16%2Fb%5E2=1
16%2Fb%5E2=1-%2836%2F100%29
16%2Fb%5E2=64%2F100%29
b%5E2=100%2A16%2F64=25
equation of given ellipse:x%5E2%2F100%2By%5E2%2F25=1