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Question 144052: hello
i have another question
sorry .. and thank your for your time
i'll get straight to the point
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find the center, foci, and vertices of the following elipse
[(x-3)^2]/4 + [(y+1)^2]/9 = 1
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thank you for your kindness
and your time as well
i appreciate it
i'll be looking forward to your answer
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The center of the general ellipse  is (h,k).
Since h=3 and k=-1, the center is (3,-1)
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Now we need to find the values of "a" and "b". So  ===> and  ===>
To find the vertices, simply start with the center (3,-1)
Add the value to the x-coordinate of the center to get (3+2,-1)--->(5,-1) This is the right-most vertex
Subtract the value from the x-coordinate of the center to get (3-2,-1)--->(1,-1) This is the left-most vertex
Add the value to the y-coordinate of the center to get (3,-1+3)--->(3,2) This is the top-most vertex
Subtract the value from the y-coordinate of the center to get (3,-1-3)--->(3,-4) This is the bottom-most vertex
So the vertices are (5,-1), (1,-1), (3,2), and (3,-4)
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To find the vertices, we must find the distance from the center to each of the foci
So use this formula to find the distance
 where c is the distance from the center to the focus
 Plug in and
 Square each term
 Subtract
 Take the square root of both sides
Now add this value to the y-coordinate of the center (3,-1) to get ) . This is the top-most focus.
Now subtract this value from the y-coordinate of the center (3,-1) to get ) . This is the bottom-most focus.
So the foci are and
Here's a picture to verify the answers.
 Graph of  with the vertices (green) and the foci (red)
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