SOLUTION: Hello, I wonder if someone can help me on this homework problem? Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hello, I wonder if someone can help me on this homework problem? Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch      Log On


   

Question 692187: Hello, I wonder if someone can help me on this homework problem?
Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch the graph.
{{xˆ2+4yˆ2=1}}

Thank you.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertices, foci, and eccentricity of the ellipse. Determine lengths of major and minor axes, and sketch the graph.
{{xˆ2+4yˆ2=1}}
**
Standard form of equation for an ellipse with horizontal major axis:
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, a>b, (h,k)=(x,y) coordinates of center
..
Rewrite given equation into standard form: x%5E2%2F1%2By%5E2%2F%281%2F4%29=1
center:0,0)
a^2=1
a=1
length of major axis = 2a=2
..
b^2=1/4
b=1/2
length of minor axis=2b=1
see graph below:
y=±(1/4-x^2/4)^.5