# 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?

• Hint: complete the square, and don't make any mistake with signs. Apr 1 '13 at 8:58
• If you want, you can ask another question. But this one has been answered, so please it leave it like this. Apr 1 '13 at 10:58

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 $3$.

The geometric interpretation is a circle with center $(1, -7/2)$, radius $3$ and diameter $6$:

Another form of the equation is:
$$\frac{1}{9}(x-1)^2+\frac{1}{9}(y+\frac{7}{2})^2 = 1$$

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