# SOLUTION: 1. Find the coordinates of the foci of the ellipse represented by x2 + 25y2 – 6x – 100y + 84 = 0.

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 Question 426511: 1. Find the coordinates of the foci of the ellipse represented by x2 + 25y2 – 6x – 100y + 84 = 0.Answer by lwsshak3(6505)   (Show Source): You can put this solution on YOUR website!Find the coordinates of the foci of the ellipse represented by x2 + 25y2 – 6x – 100y + 84 = 0. .. Standard form for ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1,(a>b), with (h,k)=(x,y) coordinates of center. x2+25y2-6x-100y+84=0 completing the squares (x^2-6x+9)+25(y^2-4y+4)=-84+9+100=25 (x-3)^2/25+(y-2)^2/1=1 This is an ellipse with a horizontal major axis and center at (3,2) a^2=25 a=5 length of major axis=2a=10 b^2=1 b=1 length of minor axis=2b=2 c^2=a^2-b^2=25-1=24 c=sqrt(24)=4.9 Foci on the major axis=3+-4.9 ans: Coordinates of foci:(3,-1.9) and (3,7.9) See graph of ellipse below: .. y=2+((25-(x-3)^2)/25)^.5