Question

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. 1
C. 4
D. 3

Answer 1

Correct Answer - A::B::D
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)