Find points on the line x + y + 3 = 0 that are at a distance of 5 units
from the line x + 2y + 2 = 0

If the question is "Find points on the line x + y + 3 = 0 that are at a distance of units from the line x + 2y + 2 = 0", then the solution is shown below:

Let the required point be (h, k).

As it lies on the line x + y +3 = 0,

∴h + k +3 = 0 .........(1)

Now,

length of perpendicular from (h, k) to x + 2y + 2 = 0 is units.

From equations (1) and (2), we get

h = -9, k = 6 and  h = 1, k = -4.

Therefore, the required points are (-9, 6) and (1, -4).

Hope you get this.

Cheers!