# A circle is described by the equation (x−12)^2+(y−32)^2=49. What are the coordinates for the center of the circle and the length of the radius?

Center $\left(h , k\right) = \left(12 , 32\right)$
Radius $r = 7$

#### Explanation:

The radius - center form of the equation of the circle is given:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ where $\left(h , k\right)$ the center
and $r$ the radius of the Circle.

From the given: ${\left(x - 12\right)}^{2} + {\left(y - 32\right)}^{2} = 49$

Also equivalent to ${\left(x - 12\right)}^{2} + {\left(y - 32\right)}^{2} = {7}^{2}$

clearly by inspection , center $\left(h , k\right) = \left(12 , 32\right)$

and Radius $r = 7$

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