Tangents from point ‘P’ are drawn one to each of circle x2+y2−2x+6y+1=0 ; x2+y2−2x+6y−3=0 if the tangents are perpendicular then locus of P is
x2+y2+2x−6y−12=0
x2+y2−2x−6y−12=0
x2+y2−2x+6y+12=0
x2+y2−2x+6y−12=0
centre = (1,−3)
r1=1+9−1=3
r2=1+9+3=13
(x−1)2+(y+3)2=r12+r22
⇒x2+y2−2x+6y+1+9=9+13
⇒ x2+y2−2x+6y−12=0