Question 456707: Write an equation for an ellipse with center (1,-3), vertices (1,2) and (1,-8), and co-vertices (4,-3) and (-2,-3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation for an ellipse with center (1,-3), vertices (1,2) and (1,-8), and co-vertices (4,-3) and (-2,-3).
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Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of a^2 and b^2.
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Given center at (1,-3)
Since the x-coordinates of the end points of the vertices are the same at 1, given ellipse has a vertical major axis on x=1.
length of major axis=10=2a
a=5
a^2=25
co-vertices or minor axis on y=-3
length of minor axis=6=2b
b=3
b^2=9
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Equation: (x-1)^2/9+(y+3)^2/25=1 (ans)
see graph below as a visual check on the algebra above. Note the center and length and end points of major and minor axes.
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y=(25-25(x-1)^2/9)^.5-3
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