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)
$\displaystyle
x^2-12x+36 + y^2 +4y+4 -25=0
$
$\displaystyle
(x-6)^2+(y+2)^2=5^2
$
hence the coordinates of centre are (6,-2)
and radius is 5
b)
-put the value of y from line's equation into that of circle
-solve the quadratic equation that follows
-for the values of x you get find y and the corresponding pairs
are point of intersection
Now try this yourself now