Answer:
Axis of symmetry are lines x=-6 and y=-4, center (-6,-4)
Step-by-step explanation:
Consideer the equation [tex]x^2+y^2+12x+8y=48.[/tex]
First, complete perfect squares:
[tex](x^2+12x)+(y^2+8y)=48,\\ \\(x^2+12x+36-36)+(y^2+8y+16-16)=48,\\ \\(x+6)^2+(y+4)^2-36-16=48,\\ \\(x+6)^2+(y+4)^2=100.[/tex]
This equation represents a circle with center at point (-6,-4) and radius r=10.
Axis of symmetry are lines x=-6 and y=-4 (vertical and horizontal lines passing through the center).
