Question 571730: How do I find the standard form of the equation of the ellipse with vertices (1,-1), (5,-1), (3,5), (3,-7)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How do I find the standard form of the equation of the ellipse with vertices (1,-1), (5,-1), (3,5), (3,-7)?
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Standard form of equation for an ellipse with vertical major axis:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For equation of given ellipse:
Center:(3,-1)
Length of vertical major axis=12=2a
a=6
a^2=36
..
Length of minor axis=4=2b
b=1
b^2=1
..
Equation of given ellipse:
(x-3)^2+(y+1)^2/36=1
see graph below as a visual check of above:
..
y=(36-36(x-3)^2)^.5+1
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