Decide whether or not the equation has a circle as its graph. If it​ does, give the center and the radius. If it does​ not, describe the graph.   4x^2 +4x+4y^2 + 8y-59=0

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter7: Conic Sections And Quadratic Systems
Section7.CR: Chapter Review
Problem 8E
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Decide whether or not the equation has a circle as its graph. If it​ does, give the center and the radius. If it does​ not, describe the graph.
 
4x^2 +4x+4y^2 + 8y-59=0
Expert Solution
Step 1

The given Equation is:
4x2+4x+4y2+8y-59=0

i.e.

4x2+4y2+4x+8y-59=0

x2+y2+x+2y-594=0---(1)

The general Equation of a circle is :

x2+y2+2gx+2fy+c=0

We observe that (1) is similar to x2+y2+2gx+2fy+c=0

Hence, The given Equation represents a circle.

This Equation has a circle as it's graph.

 

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