Equation of the circle given the center and the radius

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$\text{Find the equation of the circle with center at }O\left(0,7\right)\text{ and radius }r=5$.

**Answer**

$\text{The equation of the circle with center at }O\left(x_0,y_0\right)\text{ and radius }r=k \text{ is given by:}$

$\left(x-x_0\right)^2 + \left(y-y_0\right)^2=k^2$.

$\text{or, }\left(x \right)^2 + \left(y -7\right)^2=\left(5\right)^2$

$\text{or, }x^2+y^2-14y+49=25$

$\text{or, } x^2 + y^2-14y+24=0$