SOLUTION: find a b C and the center and sketch the graph of the ellipse 4x^2 + 25 y^2 +16 X - 150y + 141=0

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Question 877320: find a b C and the center and sketch the graph of the ellipse 4x^2 + 25 y^2 +16 X - 150y + 141=0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find a b C and the center and sketch the graph of the ellipse
4x^2 + 25 y^2 +16 X - 150y + 141=0
4x^2+16 x + 25 y^2 - 150y = -141
complete the square:
4(x^2+4x+4)+25(y^2-6y+9) =-141+16+225
4(x+2)^2+25(y-3)^2=100
%28x%2B2%29%5E2%2F25%2B%28y-3%29%5E2%2F4=1
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation:%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
For given ellipse:
center:(-2,3)
a^2=25
a=5
b^2=4
b=2
c^2=a^2-b^2=25-4=21
c=√21
see graph below:
y=±(4-(4/25)(x+2)^2)^.5+3