P and Q are two points on line x-y+1=0 in such way that they are 5 units far from origin find cordinates of points

5 units distance from the origin is easy to find; just using Pythagoras theorem.

x² + y² = 25

And the equation of your line rearranges to

y = x + 1

x² + (x+1)² = 25

2x² + 2x - 24 = 0

(x + 4)(x - 3) = 0

So your two points are (-4, -3) and (3, 4).

Regards

(Arun ) ( askIITians forum expert expert)