SOLUTION: whats are the vertices,foci,length of major and minor axis, and eccentricity of 9x^2+4y^2=36

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Question 980344: whats are the vertices,foci,length of major and minor axis, and eccentricity of
9x^2+4y^2=36
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!

You are given the ellipse

9x%5E2 + 4y%5E2 = 36+.

The canonical equation of this ellipse is  (see the lesson  Ellipse definition, canonical equation, characteristic points and elements  in this site)

%289%2F36%29x%5E2 + %284%2F36%29y%5E2 = 1,

or, which is the same

x%5E2%2F2%5E2 + y%5E2%2F3%5E2 = 1.


    (!!! Be aware: in this case  a=2 < b=3 !!!)


Vertices:  (-2, 0);  (2, 0);  (0, 3);  (0, -3).

Length of major axis  is   2*3 = 6;     (along the y-axis !)

Length of minor axis  is   2*2 = 4;     (along the x-axis !)

Linear eccentricity:   c = sqrt%283%5E2+-+2%5E2%29 = sqrt%289-4%29 = sqrt%285%29 =~ 2.236 (approximately).

Eccentricity: eps = sqrt%285%29%2F3 =~ 0.745 (approximately).

Foci:  (0, -c) = (0, -2.236)  and  (0, c) = (0, 2.236)

    (Foci lie in the y-axis in this case !)