Answer:
[tex](x+5)^2+(y+8)^2=6217[/tex]
Step-by-step explanation:
Hi there!
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and r is the radius
1) Plug the center of the circle into the equation
Center: (-5,-8)
[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2[/tex]
2) Determine r²
Plug in the given point (16,68)
[tex](x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2[/tex]
Therefore, r² is equal to 6217. Plug this back into [tex](x+5)^2+(y+8)^2=r^2[/tex]:
[tex](x+5)^2+(y+8)^2=6217[/tex]
I hope this helps!
