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

Answer

A, B, D

Explanation

1,2,4
Any point on x+y=1 can be taken as (t,1-t).
The equation of chord with this as midpoint is
`y(1-t)-2a(x+t)=(1-t)^(2)-4at`
It passes through (a,2a). So,
`t^(2)-2t+2a^(2)-2a+1=0`
This should have two distinct real roots. So,
Discriminant `gt0i.e.,a^(2)-alt0`
`0ltaltor0lt4alt4`
So, length of latua rectum lies in (0,4)