SOLUTION: Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse. {{{4x^2+9y^2=36y}}}

Question 813151: Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse.
***
4x^2+9y^2=36y
4x^2+9y^2-36y=0
complete the square:
4x^2+9(y^2-4y+4)=0+36
4x^2+9(y-2)^2=36
divide by 36
x^2/9+(y-2)^2/4=1
Given ellipse has a horizontal major axis.
Its standard form of equation:, a>b, (h,k)=(x,y) coordinates of center
..
center: (0,2)
a^2=9
a=3
length of horizontal major axis=2a=6
vertices: (0�a,2)=(0�3,2)=(-3,2) and (3,2)
..
b^2=4
b=2
length of minor axis=2b=4
..
c^2=a^2-b^2=9-4=5
c=√5≈2.2
foci:(0�c,2)=(0�2.2,2)=(-2.2,2) and (2.2,2)

RELATED QUESTIONS
Find the center, foci, vertices, and lengths of the major and minor axes. 16x^2 - 64x (answered by lwsshak3)

What are the coordinates of the center, the lengths of the major and minor axes,... (answered by lwsshak3,MathLover1)

How do you find the coordinates of the center and foci and the lengths of the major and... (answered by ewatrrr)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by Paul)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by venugopalramana)

Find the coordinates of the center and foci and the lengths of the major and minor axes... (answered by lynnlo)

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