<PRE><B>Question 11671</B>
 Let A = (xo,yo) ,B = (x1,y1),then  their midpoint is
  ((xo+x1)/2,(yo+y1)/2) = (0,0).
 So x1=-x0,y1=-yo.
 
 Since A,B are both on the  the parabola, 
 we have yo = {{{ 4xo^2+ 7xo -1}}}...(1) and
 -yo = {{{4xo^2- 7xo -1}}}...(2)
 
 (1)+(2): 0 = {{{ 8x0^2 -2}}}
 So, xo = 1/2 or -1/2
 and hence,yo = 4(1/4) - 7/2 - 1= -7/2 
  or yo = 7/2
 
 Let O be the origin.
 We see that  the length of AB = 2 distance of OA
 = 2{{{  sqrt((1/2)^2 + (7/2)^2) }}} 
 = 2 {{{ sqrt(50)/2}}} 
 = {{{ sqrt(50)}}} 

 Kenny
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