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Question 451966: Write the equation of the conic with the following characteristics.
Vertices (1,2)(9,2)
Co-vertices (5,1)(5,3)
How would I approach this question? I know you must find where the ellipse is centered at. You also must find A & B. A^2 = 4 and B^2 = 25 I'm assuming. Since it gives you the vertices which means that +or- 2 is equal to A, and the co vertices have +or- 5 meaning B is equal to 5. But then how do I find where the ellipse is centered at? Unless of course..you can't.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the equation of the conic with the following characteristics.
Vertices (1,2)(9,2)
Co-vertices (5,1)(5,3)
How would I approach this question? I know you must find where the ellipse is centered at. You also must find A & B. A^2 = 4 and B^2 = 25 I'm assuming. Since it gives you the vertices which means that +or- 2 is equal to A, and the co vertices have +or- 5 meaning B is equal to 5. But then how do I find where the ellipse is centered at? Unless of course..you can't.
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The best way to start in solving conic problems is to plot the given points to get some idea what its graph looks like.
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Notice in the two given (x,y) coordinates of the vertices, y is does not change which means that 2 is the y-coordinate of the center. Similarly,in the two given (x,y) coordinates of the co-vertices or minor axis, x does not change, so 5 is the x-coordinate of the center. Center, therefore, is at (5,2).
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Given coordinates of the vertices show that the vertices are on a line y=2, so it has a horizontal major axis. You can see that that the length of the major axis is the distance between the end points or x-coordinates of the vertices. Length of major axis=9-1=8
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Given coordinates of the co vertices show that the co- vertices are on a line x=5, so it is vertical. In this case the length of the co-vertices is the distance between the end points or y-coordinates of the vertices. Length of minor axis=3-1=2
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Center(5,2)
length of major axis=2a=8
a=4
a^2=16
length of minor axis=2b=4
b=2
b^2=4
You now have the information you need to write the equation of the given ellipse as follows:
y=(x-5)^2/16+(y-2)^2/4=1
See the graph below for a visual of the algebra above
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y=(4-(x-5)^2/4)^.5+2
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