TS EAMCET 2017 Code A Solved Paper

Given equation of pair of straight lines can be rewritten as
x(y−1)−1(y−1)=0
(x−1)(y−1)=0
x=1
y=1
The three concurrent lines are,
x=1‌‌.....(1)
y=1‌‌.....(2)
x+ay−3=0
since equation (1) and (2) intersect at only points namely (1,1)
therefore, this point also satisfy the equation (3)
1+a−3=0
a=2
Now the pair of line becomes,
2x2−13xy−7y2+x+23y−6=0
The acute angle between the lines is calculated as
tan‌θ=|‌‌

2√h2−ab

a+b

|
=|

‌‌ 2√(−‌‌ 13 2 )2+14 −5

|
=|−3|
=3
The angle is calculated as,\
θ=tan−1(3)
=cos−1(‌‌

1

√10

)