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=