I need to find the equations of the chords of the parabola subtending an angle of $45°$ at the vertex of $y²=4ax$ and passing through $(-6a,0)$.
How do I approach this? I don't know the slope of the lines, thus can't find the equations of the chords. I know that they pass through $(-6a,0)$ so I reckon that if I knew the slope then I would be able to find the equations by slope-point form.