AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

Let required point of intersection be (x1,y1) . Then the equation of chord of contact with respect to given circle is,
xx1+yy1−2(x+x1)−3(y+y1) +4=0
(x1−2)x+(y1−3)y+(4−3y1 −2x1)=0
Let above represent the line,
AB=4x+4y−11=0
Then,

x1−2

4

−

y1−3

4

=

4−3y1−2x1

−11

=K
Then,
x1=4K+2
y1=4K+3
And,
2x1+3y1−4=11K
From above,
8K+4+12K+9−4=11K
9K+9=0
K=−1
Thus, (x1,y1)=(−2,−1)