Question 540656: 74.) Sketch the ellipse. Identify the center, vertices, and foci.
9(x+4)^2+(y+7)^2=81
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Sketch the ellipse. Identify the center, vertices, and foci.
9(x+4)^2+(y+7)^2=81
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Standard form of equation for an 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.
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9(x+4)^2+(y+7)^2=81
divide by 81
(x+4)^2/9+(y+7)^2/81=1
center: (-4,-7)
a^2=81
a=9
vertices: (-4,-7±a)=(-4,-7±9)=(-4,2) and (-4,-16)
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b^2=9
b=3
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c^2=a^2-b^2=81-9=72
c=√72≈8.5
Foci: (-4,-7±c)=(-4,-7±8.5)=(-4,1.5) and (-4,-15.5)
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see graph below as a visual check:
y=±(81-9(x+4)^2)^.5-7
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