Find the centre and radius of the circles: (x + 5)^2 + (y – 3)^2 = 36
Find the centre and radius of the circles: (x + 5)^2 + (y – 3)^2 = 36

Given:

The condition of the given circle is \[~{{\left( x\text{ }+\text{ }5 \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{ }3 \right)}^{2}}~=\text{ }36\]

\[{{\left( x\text{ }\text{ }\left( -5 \right) \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{ }3 \right)}^{2}}~=\text{ }{{6}^{2}}~[which\text{ }is\text{ }of\text{ }the\text{ }form\text{ }{{\left( x\text{ }\text{ }h \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{ }k\text{ } \right)}^{2}}~=\text{ }{{r}^{2}}]\]

Where, \[~h\text{ }=\text{ }-5,\text{ }k\text{ }=\text{ }3\text{ }and\text{ }r\text{ }=\text{ }6\]

∴ The focal point of the given circle is \[\left( -\text{ }5,\text{ }3 \right)\]and its sweep is \[6.\]