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\end{align}  The above equation is a circle with radius $r=\sqrt{\frac{1}{4}(d^{2}+e^{2})-b}$, so $r^{2}$ must be greater than or equal to zero in order for a solution to exist. Thus,  \begin{align}  \frac{1}{4}(d^{2}+e^{2})\geq0 \frac{1}{4}(d^{2}+e^{2})-b\geq0  \end{align}  \end{proof}