Dear student,
(b,b) is a point on y=x line
y^2 = 4a(x-a) meets y=x at
=> x^2 = 4a(x-a) => x-2a)^2 = 0
=> (2a,2a) is the point and the slope of normal at this point is -1 i.e y=-x+4a is the equation of chord
y=-4a+x meets parabola at 4a(x-a) = x^2 + 16a^2 - 8ax
=> normal chord meets parabola at (10a,-6a)
focus of parabola is (2a,0)
Angle subtended by chord on focus = 90 + |tan-1 (-6/8)| => 126.870
