analytic geometry
posted by joey .
fin the center ,principal axis vertices, sketch the graph of 4x^y^2 +56 x +2y+195=0

analytic geometry 
Reiny
let's complete the square ...
4x^2 + 56x  (y^2  2y ) = 195
4(x^2 + 14x + 49)  (y^2  2y + 1) = 195 + 4(49)  1
4(x+7)^2  (y1)^2 = 0
ahh, we have a degenerated hyperbola
the hyperbola has degenerated into its asymtotes
notice we have a difference of squares = 0
so
2(x+7) + (y1) = 0 or 2(x+7)  (y1) = 0
2x + 14 + y  1 = 0 or 2x + 14  y + 1 = 0
2x + y = 13 or 2x  y = 15
the "centre" would be the intersection of the two lines.
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