The conics form of a circle with center $\left( {h,\;k} \right)$ and radius $r$ is:

${\left( {\frac{{x - h}}{r}} \right)^2} + {\left( {\frac{{y - k}}{r}} \right)^2} = 1$

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Examples

**graphing a circle**

Sketch each circle and state the:

i) center

ii) radius

**converting a circle equation to conics form by "completing the square"**

$4{x^2} + 4{y^2} + 24x - 8y + 15 = 0$**finding the equation of a circle given its properties**

Find the equation of a circle with: