SOLUTION: What is the center, vertices, co-vertices, and foci of 25x^2+y^2-100x-2y+76=0

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Question 841251: What is the center, vertices, co-vertices, and foci of 25x^2+y^2-100x-2y+76=0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What is the center, vertices, co-vertices, and foci of
25x^2+y^2-100x-2y+76=0
25x^2-100x+y^2-2y=-76
complete the square
25(x^2-4x+4)+(y^2-2y+1)=-76+100+1
25(x-2)^2+(y-1)^2=25
%28x-2%29%5E2%2B%28y-1%29%5E2%2F25=1
This is an equation of an ellipse with vertical major axis.
Its standard form:%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1,a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (2,1)
a^2=25
a=5
vertices:(2,1±a)=(2,1±5)=(2,-4) and (2,6)
..
b^2=1
b=1
co-vertices:(2±b,1)=(2±1,1)=(1,1) and (3,1)
..
c^2=a^2-b^2=25-1=24
c=√24≈4.9
Foci:(2,1±c)=(2,1±4.9)=(2,-2.9) and (2,5.9)