AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

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