Question 936512: What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse:
x^2/9 + y^2/16 =1
Found 2 solutions by lwsshak3, MathLover1:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse:
x^2/9 + y^2/16 =1
Given ellipse has a vertical major axis:
Its standard form of equation:  , a>b, (h,k)=coordinates of center
..
For given ellipse:
center:(0,0)
a^2=16
a=4
length of major axis=2a=8
b^2=9
b=3
length of minor axis=2b=6
vertices:(0,0±a)=(0,0±4)=(0,-4) and (0,4)
co-vertices:(0±b,0)=(0±3,0)=(-3,0) and (3,0)
foci:
c^2=a^2-b^2=16-9=7
c=√7≈2.6
foci:(0,0±c)=(0,0±2.6)=(0,-2.6) and (0,2.6)
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! The standard form of the equation of an ellipse is:
 for horizontal ellipses, and
 for vertical ellipses
In these equations, the " " and the " " are the  and  coordinates, respectively, of the center.
here is your ellipse:
from given we know that  ,  ; so, center is at origin ( ,)
we also know that major axis is vertical and
semi-major axis length is 
semi-minor axis length is 
the vertices will be " " distance above and below the center:
vertices (,  ) | (, )
The co-vertices are right and left:
( , ) | ( ,)
The distance from the center to each focus is called " ". The "" is not in the standard form of the equation for an ellipse. But there is a fixed relationship between the "", the " " and the "" values:
foci: | (,  ) | (,  )
or approximately (,  ) | (,  )
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