Math Help - circles help please

x^2-12x+y^2+4y+15=0

a) specifies a circle. find its centre and radius.

b) Find the coordinates of any points at which the circle in part (a) intersects line y=x-9

x^2-12x+y^2+4y+15=0

a) specifies a circle. find its centre and radius.

b) Find the coordinates of any points at which the circle in part (a) intersects line y=x-9
a)
$
x^2-12x+36 + y^2 +4y+4 -25=0
$

$
(x-6)^2+(y+2)^2=5^2
$

hence the coordinates of centre are (6,-2)