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Question 459114: how do I graph 25(x+4)^2 + (y-3)^2 =25
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do I graph 25(x+4)^2 + (y-3)^2 =25
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25(x+4)^2 + (y-3)^2 =25
divide by 25
(x+4)^2 + (y-3)^2/25 =1
This equation is an ellipse with a vertical major axis. (second form listed below)
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Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of 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.
The difference between the two forms is the interchange of a^2 and b^2.
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for given problem:
center: (-4,3)
a^2=25
a=5
length of major axis=2a=10
vertices: (-4,3±a)=(-4,3±5)
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b^2=1
b=1
length of minor axis=2b=2
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See graph below as a visual check on the answers.
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y=(25-25(x+4)^2)^.5+3
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