Find all points having an x coordinate of 1 whose distance from the point (-3,-1) is 5.

The distance between the points (x₁,y₁) and (x₂,y₂) is calculated through the equation,
                              d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)
From our given, we have the point (-3,-1) and (1,y). Substituting these to the equation,
                              5 = sqrt ((-3 - 1)² + (-1 - y)²)
Squaring both sides,
                            25 = (-3 - 1)² + (-1 - y)²

The values of y from the equation are 2 and -4. 

The answers are therefore: (a) (1, 2) and (b) (1, -4).