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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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