# Find the coordinates of the centre radius of each of the following circle x^2+y^2+6x-8y-24=0

$x^2+y^2+6x-8y-24=0\*Given:The\;equation\;of\;the\;circle\;is\; x^2+y^2+6x-8y-24=0..eq(1)\\*We\;know\;that\;for\;a\;circle\; x^2+y^2+2ax+2by+c=0..eq(2)\\*Centre=(-a,-b)\\*So\;by\; comparing\;equation\;eq(1)\;and\;eq(2)\\*Centre=(\frac{-6}{2}, \frac{-(-8)}{2})=(-3,4)\\*Radius=\sqrt{a^2+b^2-c}\\* \Rightarrow\;\sqrt{32+42-(-24)}\\*\Rightarrow\;\sqrt{9+16+24}\\* \Rightarrow\;\sqrt{49}\\*\Rightarrow\;7\\*\therefore\;The\; centre\;of\;the\;circle\;is\;(-3,4)\;and\;the\;radius\;is\;7.$

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