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Answer 1 · 2016-08-26T14:17:26

We get two pts.

#P_1(1,12/5), and, P_2(-3,16/5)# satisfying the given cond.

Let the given lines be

# l :x+5y=13, and, l' : 12x-5y+26=0#

Let the reqd. pt. be #P(h,k)#.

Given #P in l, rArr h+5k=13....................(1)#.

Also, (#bot#)distance from #P# to #l'# is #2#.

#rArr |12h-5k+26|/sqrt(12^2+(-5)^2)=2#

#:. |12h-5k+26|=26, or, 12h-5k+26=+-26#

#:. 12h-5k=0... ...(2'), or, 12h-5k=-52... ...(2'')#

Solving #(1),(2'),(2'')#, we get two pts.

#P_1(1,12/5), and, P_2(-3,16/5)# satisfying the given cond.

Enjoy Maths.!