Question 554822: write an equation of an ellipse whose vertices are(-3,0) and (3,0) and whose co-vertices are(0,-6) and (0,6). Graph the Ellipse.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write an equation of an ellipse whose vertices are(-3,0) and (3,0) and whose co-vertices are(0,-6) and (0,6). Graph the Ellipse.
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I think you mis-labeled the vertices. Vertices are end-points of the major axis. Co-vertices are the end-points of the minor axis which are shorter than the major axis. I will assume you meant the vertices to be (0,-6) and (0,6) and the co-vertices to be (-3,0) and (3,0)
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What you have here is an ellipse with vertical major axis of the standard form of equation:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For given ellipse:
center:
note that mid points of vertices and co-vertices are zero
center:(0,0)
length of vertices=12=2a
a=6
a^2=36
length of co-vertices=6=2b
b=3
b^2=9
Equation of ellipse:
x^2/9+y^2/36=1
see graph below:
y=±(36-4x^2)^.5
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