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)|=`

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

`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`