



 
Hi Jamie, I don't know what you mean by the Greek method but I can show you how I would solve this problem. First rewrite the equation as \[\left[ x^2  4x\right] + \left[y^2 + 6y \right] = 4.\] Next I would complete the square for each of the expressions in square brackets to get an expression of the form \[(x  a)^2 + (y  b)^2 = r^{2}.\] This is an expression for the circle with center $(a ,b)$ and radius $r.$ Thus you know the coordinates of the center of the circle. To complete this problem use that fact that for a circle with center $O$ and a point $P$ on the circumference of the circle, the line segment from $O$ to $P$ is perpendicular to the tangent to the circle at $P.$ Write back if you have problems completing the problem. Tell us what you have done and we will try to help,  


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