EXPLANATION
Considering the equation x^2 + y^2 + 4x = 0
As we already know, the circle equation with a radius r, centered at (a,b) is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Rewrite x^2 + y^2 + 4x = 0 in the form of the standard circle equation:
Group x-variables and y-variables together:
[tex](x^2+4x)+y^2=0[/tex]Convert x to square form:
[tex](x^2+4x+4)+y^2=4[/tex]Convert to square form:
[tex](x+2)^2+y^2=4[/tex]Refine 4:
[tex](x+2)^2+y^2=4[/tex]Rewrite in standard form:
[tex](x-(-2))^2+(y-0)^2=2^2[/tex]Therefore the circle properties are:
center: (a,b)=(-2,0) radius: r=2
Finally, drawing the graph of the equation:
