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Tju [1.3M]3 years ago

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Write the standard form of the equation of the circle with the given characteristics. Center: (3, 5); Solution point: (−2, 17)

Angelina_Jolie [31]

$\text{we know that the general equation of the circle is }\\
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(x-h)^2+(y-k)^2=r^2\\
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\text{where, (h,k) is the center of the circle and r is the radius.}\\
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\text{Given that the centered of the circle is at }(h,k)=(3,5)\\
\text{and a solution point on circle is (-2,17).}\\
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\text{so the radius of the circle will be the distance between center and the }$

$\text{solution point. so using the distance formula, we have}\\
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\text{Radius, }r=\sqrt{(-2-3)^2+(17-5)^2}\\
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\Rightarrow r=\sqrt{25+144}\\
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\Rightarrow r=\sqrt{169}\\
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\Rightarrow r=13\\
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\text{Hence using the standard for of circle, equation of circle with center}\\
(h,k)=(3,5) \text{ and radius r=13 is}\\
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(x-3)^2+(y-5)^2=(13)^2\\
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\Rightarrow (x-3)^2+(y-5)^2=169$