## Question

###### DiscoveR: Circle, Point, or Empty Set? Complete thesquares in the general equation $x^{2}+a x+y^{2}+b y+c=0$,and simplify the result as much as possible. Under whatconditions on the coefficients $a, b,$ and $c$ does this equationrepresent a circle? A single point? The empty set? In thecase in which the equation does represent a circle, find itscenter and radius.

DiscoveR: Circle, Point, or Empty Set? Complete the squares in the general equation $x^{2}+a x+y^{2}+b y+c=0$, and simplify the result as much as possible. Under what conditions on the coefficients $a, b,$ and $c$ does this equation represent a circle? A single point? The empty set? In the case in which the equation does represent a circle, find its center and radius.

## Answers

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