SOLUTION: Find the center, vertices, foci and eccentricity of the ellipse x^2+9y^2=36.

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Question 1087920: Find the center, vertices, foci and eccentricity of the ellipse x^2+9y^2=36.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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x%5E2+%2B+9y%5E2 = 36  is equivalent to  x%5E2%2F36 + y%5E2%2F4 = 1


The center is at (0,0), the origin of the coordinate center.

The major axis is along the x-axis, while the minor axis is along the y-axis.

The major axis is  a = 6 = sqrt%2836%29 units long.

The minor axis is  b = 2 = sqrt%284%29 units long.

The vertices are (6,0) and (-6,0), while the co-vertices are (0,2) and (0,-2).

The linear eccentricity is c = sqrt%28a%5E2+-+b%5E2%29 = sqrt%286%5E2+-+2%5E2%29 = sqrt%2832%29 = 4%2Asqrt%282%29.

The foci of the ellipse are  (-4%2Asqrt%282%29,0)  and  (4%2Asqrt%282%29,0).



Figure. Ellipse x2%2F36 + y%5E2%2F4 = 1

See the lessons
    - Ellipse definition, canonical equation, characteristic points and elements

    - Standard equation of an ellipse
    - Identify elements of an ellipse given by its standard equation
    - Find the standard equation of an ellipse given by its elements
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".