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Question 768359: Identify the conic section that matches the equation shown below. Then, identify the center and foci.
5x2 + 7y2 + 50x - 28y + 118 = 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Identify the conic section that matches the equation shown below. Then, identify the center and foci.
5x2 + 7y2 + 50x - 28y + 118 = 0
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5x^2+7y^2+50x-28y+118=0
5x^2+50x+7y^2-28y+118=0
complete the square
5(x^2+10x+25)+7(y^2-4y+4)=-118+125+28
5(x+5)^2+7(y-2)^2=35
(x+5)^2/7+(y-2)^2/5=1
This is an equation of an ellipse with horizontal major axis.
Its standard form:  , (h,k)=(x,y) coordinates of center
For given ellipse:
center: (-5,2)
a^2=7
b^2=5
c^2=a^2-b^2=7-5=2
c=√2
foci: (-5±c,2)=(-5±√2,2)=(-5+√2,2) and (-5-√2,2)
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