AP EAPCET 25-Aug-2021 Shift 2 Paper

Since, we know that, point of intersection of pairs of line represented by
ax2+2hyx+by2+2gx+2fy+c=0 is
(

hf−bg

ab−h2

,

gh−af

ab−h2

)
For the lines, x2+2xy−35y2−4x+44y−12=0
a=1,h=1,b=−35,g=−2,f=22 and c=−12
∴ (

hf−bg

ab−h2

,

gh−af

ab−h2

)
=(

1×22−70

−35−1

,

−2−22

−35−1

)=(

−48

−36

,

−24

−36

) =(

4

3

,

2

3

)
∵ Lines are concurrent, hence
(

4

3

,

2

3

) must satisfy 5x+ky−8=0
5(

4

3

)+k(

2

3

)=8
20+2k=24
⇒2k=4
⇒ k = 2