to #1.:

Calculate the coordinates of the centre of the circle by completing the squares:

The line in question has to pass through (2, -3) and the origin.

You should get:

to #2:

Calculate the coordinates of the centre of the circle by completing the squares:

There are two cases possible if the x-axis and a straight line include an angle of 45°: The slope of the line can be m = 1 or m = -1

Use the point-slope-formula to calculate the equation of the line:

a) m = 1:

b) m = -1