DISCOVER: Circle, Point, or Empty Set? Complete the squares in the general equation x? + ax + y + by + c = 0, and sim- plify the result as much as possible. Under what conditions on the coefficients a, b, and c does this equation represent a cir- cle? A single point? The empty set? In the case in which the equation does represent a circle, find its center and radius.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Question
DISCOVER: Circle, Point, or Empty Set? Complete the squares
in the general equation x? + ax + y + by + c = 0, and sim-
plify the result as much as possible. Under what conditions on
the coefficients a, b, and c does this equation represent a cir-
cle? A single point? The empty set? In the case in which the
equation does represent a circle, find its center and radius.
Transcribed Image Text:DISCOVER: Circle, Point, or Empty Set? Complete the squares in the general equation x? + ax + y + by + c = 0, and sim- plify the result as much as possible. Under what conditions on the coefficients a, b, and c does this equation represent a cir- cle? 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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