If two distinct chords of a parabola `y^2=4ax` , passing through `(a,2a)` are bisected by the line `x+y=1` ,then length of latus rectum can be a) 2 b) 7 c) 4 d) 5

Options

A. 9
B. 3
C. 4
D. 5

Answer

B

Explanation

Any point on `x +y =1` is `(t,1-t)`.
Thus, equation of chord with this point as mid point is `y (1-t) -2a (x+t) = (1-t)^(2) - 4at`.
It passes through `(a,2a)`, so `t^(2) -t +2a^(2) -2a +1 =0`. This should have two distinct real roots
`:. a^(2) -a lt 0 rArr 0 lt a lt 1 rArr 0 4a lt 4`