Let the coordinates of a point whose distance from 4x+3y=10 are (α,β). Then,
|4α+3β−10|
√42+32
=1 ⇒|4α+3(4−α)−10|=5 [∵α,β lies on line x+y=4] ⇒|4α+12−3α−10|=5 ⇒|α+2|=5⇒α+2=±5 ⇒α+2=5 or α+2=−5 α=3,α=−7 If α=3, then β=1 If α=−7, then β=11 d=√(3+7)2+(1−11)2=√100+100 =√200=10√2 units
