Find the coordinates of the point(s) on the line x+y+3=0, whose distance from the line x+2y+2 = 0 is 5^0.5.

Let the coordinates of the required point be (x₁, y₁).

It is given that this point lies on x + y + 3 = 0

Therefore, x₁ + y₁ + 3 = 0  .... (1)

Now, length of the perpendicular from (x₁, y₁) to x + 2y + 2 = 0 is √5.

 On solving equation (1) and (2), we get

x₁ = -9, y₁ = 6 and x₁ = 1, y₁ = -4

So, the coordinates of the required point are (-9, 6) and (1, -4).