What is the standard form of the equation of a circle with a center (7, 3) and a diameter of 24?

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What is the standard form of the equation of a circle with a center (7, 3) and a diameter of 24?

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Answer 1 · 2015-11-29T06:53:41

${(x - 7)}^{2} + {(y - 3)}^{2} = 144$ $(x - 7)^2 + (y-3)^2 = 144$

Explanation:

The standard form of a circle centered at $(x_{1}, y_{1})$ $(x_1, y_1)$ with radius $r$ $r$ is
${(x - x_{1})}_{1}^{2} + {(y - y_{1})}_{1}^{2} = r^{2}$ $(x-x_1)^2 + (y-y_1)^2 = r^2$

The diameter of a circle is twice its radius. Therefore a circle with diameter $24$ $24$ will have radius $12$ $12$ . As $12^{2} = 144$ $12^2 = 144$ , centering the circle at $(7, 3)$ $(7, 3)$ gives us

${(x - 7)}^{2} + {(y - 3)}^{2} = 144$ $(x - 7)^2 + (y-3)^2 = 144$

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What is the standard form of the equation of a circle with a center (7, 3) and a diameter of 24?

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