# Write the equation of the circle described. a. Center at the origin, containing the point (-6, -8) b. Center (7, 5), containing the point (3, -2).

Write the equation of the circle described.
a. Center at the origin, containing the point (-6, -8)
b. Center (7, 5), containing the point (3, -2).
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Use the standard equation of a circle with center (h,k) and radius r:
${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}$
a.Using $\left(h,k\right)=\left(0,0\right)$ and $\left(x,y\right)=\left(-6,-8\right)$, solve for ${r}^{2}$:
${\left(-6-0\right)}^{2}+{\left(-8-0\right)}^{2}={r}^{2}$
$36+64={r}^{2}$
$100={r}^{2}$
So, the equation of the circle is:
${\left(x-0\right)}^{2}+{\left(y-0\right)}^{2}=100$
${x}^{2}+{y}^{2}=100$
b.Using $\left(h,k\right)=\left(7,5\right)$ and $\left(x,y\right)=\left(3,-2\right)$, solve for ${r}^{2}$:
${\left(3-7\right)}^{2}+{\left(-2-5\right)}^{2}={r}^{2}$
$16+49={r}^{2}$
$65={r}^{2}$
So, the equation of the circle is:
${\left(x-7\right)}^{2}+{\left(y-5\right)}^{2}=65$

Jeffrey Jordon