Answer:
[tex](x-2)^2+(y-6)^2=169[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
- Center = (2, 6)
- Point on the circle = (-3, 18)
Substitute the given center and point into the equation of a circle formula and solve for r²:
[tex]\implies (-3-2)^2+(18-6)^2=r^2[/tex]
[tex]\implies (-5)^2+(12)^2=r^2[/tex]
[tex]\implies 25+144=r^2[/tex]
[tex]\implies 169=r^2[/tex]
[tex]\implies r^2=169[/tex]
Therefore, the standard form of the equation of the circle with the given characteristics is:
[tex](x-2)^2+(y-6)^2=169[/tex]
