AP EAPCET 19-Aug-2021 Shift 1 Paper

The distance of point A from the line will be equal to the distance of B from line.
∴

|2+6+4|

√13

=

|2α+3β+4|

√13

⇒2α+3β+4=±12
⇒2α+3β=8 ...(i)
2α+3β=−16 ...(ii)
Also, the line joining A and B is perpendicular to
2x+3y+4=0
⇒ Product of slopes =−1
∴

β−2

α−1

×(

−2

3

)=−1
⇒2β−4=3α−3
⇒2β−3α=1 ...(iii)
Solving Eqs. (ii) and (iii), we have
α=

−35

13

.β=

−46

13

∴13α+13β=−35−46=−81