Question 430265: determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148?
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Standard form of ellipse for horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
Standard form of ellipse for vertical major axis: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b)
In both forms, (h,k) represent the (x,y) coordinates of the center.
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18x2+y2_108x+4y+148
completing the squares:
18(x^2-6x+9)+(y^2+4y+4)=-148+162+4=18
divide by 18
(x-3)^2/1+(y+2)^2/18=1
change positions
(y+2)^2/18+(x-3)^2/1=1
This is an ellipse with a vertical major axis(second form described above)
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center: (3,-2)
a^2=18
a=sqrt(18)=4.24..
b=1
b^2=1
c^2=a^2-b^2=18-1=17
c=sqrt(17)=4.12..
Vertices are on the major axis on the line,x=3, -2+-4.24 or (3,2.24) and (3,-6.24)
Similarly, foci are on the major axis,-2+-4.12 or (3,2.12) and (3,-6.12)
Graph below can visually confirm the answers obtained.
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y=+-((1-(x-3)^2)18)^.5-2
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