Answer:
[tex](x-5)^2+(y-7)^2=50[/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
Plug in the center (5,7)
[tex](x-5)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,8) to solve for r²
[tex](-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2[/tex]
Therefore, r² is equal to 50. Plug this back into [tex](x-5)^2+(y-7)^2=r^2[/tex]
[tex](x-5)^2+(y-7)^2=50[/tex]
I hope this helps!
