SOLUTION: consider the ellipse 9x^2+49y^2=9 Its vertices are (0,+or-A) Its Foci are (0,+or-B) Its eccentricity is? The length of its major and minor axis are?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: consider the ellipse 9x^2+49y^2=9 Its vertices are (0,+or-A) Its Foci are (0,+or-B) Its eccentricity is? The length of its major and minor axis are?      Log On


   

Question 743930: consider the ellipse 9x^2+49y^2=9
Its vertices are (0,+or-A)
Its Foci are (0,+or-B)
Its eccentricity is?
The length of its major and minor axis are?
Answer by lwsshak3(11628) About Me  (Show Source):
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consider the ellipse 9x^2+49y^2=9
Its vertices are (0,+or-A)
Its Foci are (0,+or-B)
Its eccentricity is?
The length of its major and minor axis are?
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I will use standard notation which you can convert to your own notation:
Given 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,(a>b), (h,k)=(x,y) coordinates of center.
9x%5E2%2B49y%5E2=9
x%5E2%2By%5E2%2F%289%2F49%29=1
a^2=1
a=1
length of major axis=2a=2
b^2=9/49
b=3/7
length of minor axis=2b=6/7≈0.8571
c^2=a^2-b^2=1-9/49=49/49-9/49=40/49
c=√(40/49)≈0.9035
eccentricity=c/a=0.9035/1≈0.9035