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# 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 what...

## 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.

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