Answer:
[tex](x+5)^2+(y-6)^2=41[/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 [tex](h,k)[/tex] and r is the radius
1) Plug in the center (-5,6)
[tex](x-(-5))^2+(y-6)^2=r^2\\(x+5)^2+(y-6)^2=r^2[/tex]
2) Plug in the given point (-1,1) and solve for r²
[tex](-1+5)^2+(1-6)^2=r^2\\(4)^2+(-5)^2=r^2\\16+25=r^2\\41=r^2[/tex]
Therefore, r² is 41. Plug this back into [tex](x+5)^2+(y-6)^2=r^2[/tex]:
[tex](x+5)^2+(y-6)^2=41[/tex]
I hope this helps!
