# Find the centre and radius of the circle $(x+5)^2 + (y-3)^2 = 36$

$\begin{array}{1 1}centre = (-5,3), radius = 6 \\ centre = (5,-3), radius = 6 \\ centre = (-6,4), radius = 1 \\ centre = (-5,-3), radius = 6 \end{array}$

Toolbox:
• Given C (h, k) be the centre and r the radius of circle. Let P(x, y) be any point on the circle. Then, by the definition, | CP | = r . By the distance formula, we have, $(x-h)^2+(y-k)^2=r^2$
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Given: the equation of the circle, we need to rewrite it in the form $(x-h)^2+(y-k)^2=r^2$, so that we can determine the centre as (h,k) and radius as $r$
Given $(x+5)^2 + (y-3)^2 = 36$
This is an easy one where we can immediately see that $r = \sqrt 36 = 6$ and $h = -5, k = 3$