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Write the standard form of the equation of the circle with the given characteristics.
Center: (2, 6); Solution point: (-3, 18)

User Tamy
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1 Answer

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Answer:


(x-2)^2+(y-6)^2=169

Explanation:


\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}}

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:


\implies (-3-2)^2+(18-6)^2=r^2


\implies (-5)^2+(12)^2=r^2


\implies 25+144=r^2


\implies 169=r^2


\implies r^2=169

Therefore, the standard form of the equation of the circle with the given characteristics is:


(x-2)^2+(y-6)^2=169

User FabienChn
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