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If two distinct chords of a parabola y^2...

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

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equation of chord with mid-point given:
`y(1-t)-2a(x+t)=(1-t)^2-4at`
`2a(1-t)-2a(a+t)=(1-t)^2-4at`
`t^2-2t+1+2a^2-2a)=0`
`4-4(1+2a^2-2a)>0`
`1-1-2a^2+2a>0`
`-2a(a-1)>0`
`a<0`
...
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