Question

Question #5bd8d

Answer 1

We get two pts.

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

Explanation:

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.!