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  • If two distinct chords of a parabola , passing through <img alt="(a, 2 a)" src="https://entr

If two distinct chords of a parabola y^2=4 a x, passing through (a, 2 a) are bisected on the line x+y=1, then length of the latus rectum can be less than..........

Option: 1

2


Option: 2

4


Option: 3

1


Option: 4

None


Answers (1)

best_answer

Any point on the line x+y=1 can be taken (t, 1-t) equation of the chord, with this as mid point is 

y(1-t)-2 a(x+t)=(1-t)^2-4 a t, it passes through (a, 2 a) So, t^2-2 t+2 a^2-2 a+1=0, this should have two distinct real roots so, a^2-a<0,0<a<1 so, length of latusrectum < 4. 

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