If the chord of contact of the point P (1,1) with respect to the circle S=x^2+y^2+4 x+6 y-3=0 meet the circle S =0 at A and B , then the area of PAB is

Step-by-step solution

aligned & S=x^2+y^2+4 x+6 y-3=0 & (x+2)^2+(y+2)^2=4^2 aligned aligned & OP ^2= AP ^2+ OA ^2 5^2=4^2+ AP ^2 AP =3 & Let AOP = BOP = & = 3 5 = 4 5 & 2 =2 =2 3 5 4 5 = 24 25 & AOB = 1 2 OA OB 2 & = 1 2 4 4 24 25 = 192 25 & OAP = AOP - AOQ & = AOP - AOB 2 & = 1 2 4 3- 96 25 =6- 96 25 = 54 25 & PAB =2 OAP =2 54 25 = 108 25 aligned