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Question 448306: need to find the center and forci and the lengths of major axes and minor axes for the ellipse and graph it
x^2 + 25y^2 -8x + 100y+91=0
Show me how to do it dont just give me the answer please:)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! need to find the center and forci and the lengths of major axes and minor axes for the ellipse and graph it
x^2 + 25y^2 -8x + 100y+91=0
Show me how to do it dont just give me the answer please:)
..
Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1 (a>b)
x^2 + 25y^2 -8x + 100y+91=0
completing the square
(x^2-8x+16)+25(y^2+4y+4)=-91+16+100=25
(x-4)^2+25(y+2)^2=25
divide by 25
(x-4)^2/25+(y+2)^2/1=1
This is an ellipse with center at (4,-2) and a horizontal major axis. (standard form first listed above)
a^2=25
a=5
b^2=1
b=1
c^2=a^2-b^2=5-1=4
c=2
Length of major axis = 2a=10
End points of major axis, (9,-2), (-1,-2) (also, called the vertices)
Length of minor axis=2b=2
End points of minor axis, (4,-3), (4,-1)
Foci,(2,-2), (6-2)
See graph below for visual evidence of parameters above
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y=(1-(x-4)^2/25)^.5-2
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