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Chords AB and CD of parabola y^(2)=8x intersect at E(2,0). Tangents at A and B intersect at P(x_(1),y_(1)) and those at C and D intersect at Q (x_(2),y_(2)).Then |x_(1)-x_(2)|=

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Solution :`because ""y+z=a+2x`
`""z+x=b+2y`
`""x+y=c+2z`
`THEREFORE "" "by adding we get "a+b+c=0`
ALSO `b=4a+(c)/(4)implies 16a-4b+c=0`
implies x = 1 and `x = - 4` are roots of equation `AX^(2)+bx+c=0`
`therefore "" "sum of roots" = 1+(-4)=-3`


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