<s>[INST] Interpret the equation $17+28y+4x^2+4y^2=8x$ geometrically 
Interpret the equation geometrically:
  $$17+28y+4x^2+4y^2=8x$$

I have drawn the bend and now I got the expression $(y-2)=(1-x)^2$ but that is the wrong expression. What should it be?
 [/INST] Bring all terms onto one side. Club all the 'x' terms together and all the 'y' terms together.
You get:
$(4x^2 - 8x) + (4y^2 + 28y) + 17 = 0$
Simplify the above equation as :
$(4x^2 - 8x + 4) + (4y^2 + 28y + 49) + 13-49 = 0$
$4{(x-1)}^2 + 4{(y+7/2)}^2 = 36$
${(x-1)}^2 + {(y+7/2)}^2 = 3^2$
Hence it is a circle with center $(1,-7/2)$ and radius $3$.
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