Two distinct chords
If two distinct chords of a parabola = , passing through (a,2a) are bisected by the line ,then length of latus rectum can be
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1 solution
Any point on the line x+ y= 1 can betaken as(t,1-t)
Equation of chord with this as midpoint is
y(1-t) -2a(x+t) = ( 1 − t ) 2 -4at
It passes through (a,2a)
therefore, t 2 -2t+2 a 2 -2a+1=0
This should have two distinct real roots so
a 2 -a<0
0<a<1
length of latus rectum < 4
So ,the answer is 2