 Hi and welcome to a session where I will discuss the following question. The question says find the points on the x-axis whose distances from the line x y 3 plus y by 4 is equal to 1 at 4 units. Before solving this question we should know the formula for finding the distance of a point from a line. The equation of straight line is E y plus C is equal to 0 and P is a point having coordinates x 1 y 1. The distance of this point from this line that is D is given by mod of x 1 plus B y 1 plus C upon square root of A square plus B square. Again with the solution given equation of line is x by 3 plus y by 4 is equal to 1. Right, now this in height is equal to 12 times 4 x plus 3 y minus 12 is equal to 0. Now on comparing this equation with A x plus B y plus C is equal to 0 we find that A is equal to 4, B is equal to 3 and C is equal to minus 12. We have to find the points on the x-axis whose distances from the line x by 3 plus y by 4 is equal to 1 at 4 units. Now any point on x-axis is of the form find the distance of the point x 0 from the line 4 x plus 3 y minus 12 is equal to 0. We have learnt above that the distance of the point P having coordinates x 1 y 1 from the line A x plus B y plus C is equal to 0 is given by mod of A x 1 plus B y 1 plus C upon square root of A square plus B square. Now here A is equal to 4, B is equal to 3 and C is equal to minus 12 and x 1 y 1 is x 0. So let us now substitute all these values in the above formula. By substituting the values we get mod of 4 into x plus 3 into 0 minus 12 upon square root of 4 square plus 3 square. Now it is given to us that this distance is equal to 4 units. Now this implies 4 x minus 12 that is mod of 4 x minus 12 upon square root of 16 plus 9 is equal to 4. This implies mod of 4 x minus 12 upon 5 is equal to 4. This implies 4 x minus 12 mod is equal to 20. This implies 4 x minus 12 is equal to 20 or minus of 4 x minus 12 is equal to 20. Now this implies 4 x is equal to 32 or this implies minus 4 x is equal to 8. Now this implies x is equal to 8 or minus 4 x is equal to 8 implies x is equal to minus 2. Now the points on the x axis is of the form x 0. So the required points are minus 2 0 and 8 0. This is our required answer. So this completes the session. Bye and take care.