If the line y = x -1 bisects two chords of the parabola y 2 = 4bx which are passing through the point (b, -2b), then the length of the latus rectum can be equal to
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Any point on y = x-1 can be taken as (h, h- 1)
Taking (h, h - 1) as the midpoint of chord, the equation of chord is
y (h -1) - 
Which passes through the point (6, —26)
-26 (h - 1) – 2b (b + h) = h 2 - 2h + 1 - 4bh
h 2 - 2h + (2b 2 – 2b + 1) = 0
As, above equation has two real roots, hence,
(-2) 2 -4(1)(2b 2 -2b+l) >0
2b 2 – 2b < 0 
b< 1 
4b< 4
length of latus rectum is less than 4
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