What is the equation of the circle with a center at $(2, 6)$ $(2 ,6 )$ and a radius of $3$ $3$ ?

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What is the equation of the circle with a center at $(2, 6)$ $(2 ,6 )$ and a radius of $3$ $3$ ?

1 Answer

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Answer 1 · 2016-01-31T20:46:24

The equation of the circle would be ${(x - 2)}^{2} + {(y - 6)}^{2} = 3^{2}$ $(x - 2)^2 + (y - 6)^2 = 3^2$
or ${(x - 2)}^{2} + {(y - 6)}^{2} = 9$ $(x - 2)^2 + (y - 6)^2 = 9$

Explanation:

The equations of the circle is
${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x - h)^2 + (y- k)^2 = r^2$
where h is the x of the center of the circle and k is the y of the center of the circle, and r is the radius.

(2,6) radus is 3

h = 2
k = 6
r = 3

plug in the values
${(x - 2)}^{2} + {(y - 6)}^{2} = 3^{2}$ $(x - 2)^2 + (y- 6)^2 = 3^2$
simplify
${(x + 4)}^{2} + {(y - 6)}^{2} = 9$ $(x + 4)^2 + (y- 6)^2 = 9$

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