The point P is taken as. S1(a,b)=S2(a,b) a2+b2+2ga+2fb+c=a2+b2+
3
2
a+4b+c=0 a(2g−
3
2
)+b(2f−4)=0 This is locus of radical axis. So. x(2g−
3
2
)+y(2f−4)=0 is the radical axis of the given circles. This touched the curve of equation x2+y2+2x+2y+1=0 The radius of the circle is given as, r=√12+12−1=1 The centre of the circle is (-1,-1) The radius of thee circle is equal to distance between centre and touching point.