The chord of contact of two tangents drawn from the point P(a,b) to the given circle is xa+yb−(x+a)−3(y+b)−8=0 (a−1)x+(b−3)y−(a+3b+8)=0 This line coincides with 5x+y+1=0 Therefore,
a−1
5
=
b−3
1
=
−(a+3b+8)
1
So, a−1=5(a+3b+8) 6a+15b=−39 2a+5b=−13 And, b−3=−a−3b−8 a+4b=−5 On solving the equations, a=−9 b=1 Therefore, 5a+b=5(−9)+1 =−45+1 =−44