SOLUTION: 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
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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.
..
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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