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

Question 426511: 1. Find the coordinates of the foci of the ellipse represented by x2 + 25y2 � 6x � 100y + 84 = 0.
Answer by lwsshak3(11628) (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

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