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

Question 980344: whats are the vertices,foci,length of major and minor axis, and eccentricity of
9x^2+4y^2=36

Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!

You are given the ellipse

+ = .

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

+ = ,

or, which is the same

+ = .

    (!!! 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 = = = =~ 2.236 (approximately).

Eccentricity: = =~ 0.745 (approximately).

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

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

RELATED QUESTIONS
consider the ellipse 9x^2+49y^2=9 Its vertices are (0,+or-A) Its Foci are (0,+or-B)... (answered by lwsshak3)

How do I identify the center, co-vertices, foci, length of major axis, length of minor... (answered by lwsshak3)

I need help finding a) vertex b) vertices c) foci d) major axis and e) minor axis of the... (answered by Ed Parker)

Identify the center, vertices, co-vertices, foci, length of the major axis, length of the (answered by lwsshak3)

x^2/25+y^2/16=1 what are its vertices,foci,eccentricty of the ellipse? length of major (answered by ikleyn)

For the following ellipse: (x + 2)2 + (y + 2)2 = 1 (answered by Boreal)

find the foci, length of the major axis, and length of the minor axis for the ellips x^2... (answered by lwsshak3)

Hello, I wonder if someone can help me on this homework problem? Find the vertices,... (answered by lwsshak3)

find the answers of the following: ellipse: 4X^2+y^2+8X-4y-92=0 find its... (answered by jsmallt9)