Question 502616: identify the center, vertices, length of the major axis and of the minor axis of each. then sketch the graph:
4x^2+y^2+40x-8y+112=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! identify the center, vertices, length of the major axis and of the minor axis of each. then sketch the graph:
4x^2+y^2+40x-8y+112=0
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4x^2+y^2+40x-8y+112=0
complete the square
4(x^2+10x+25)+(y^2-8y+16)=-112+100+116=104
4(x+5)^2+(y-4)^2=104
(x+5)^2/26+(y-4)^2/104=1
This is an ellipse with vertical major axis of the form: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
For given equation:
Center: (-5, 4)
b^2=26
b=√26
length of minor axis=2b=2√26=10.2
..
a^2=104
a=√104=10.2
length of vertical major axis=2a=2√104=20.4
vertices (end points of vertical major axis)
vertices=(-5, 4±a)=(-5, 4±√104)=(-5, 4+√104) and (-5, 4-√104)=(-5, 14.2) and (-5, -6.2)
See graph below as a visual check on answers:
..
y=(104-104(x+5)^2/26)^.5+4
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