parabolas and point slope

[pradababe128]

Consider a parabola with equation y = 4 ? x squared
and a point P : (a, b) in its interior. A line with slope m through P intersects the parabola at points A and B. Find
|xA ? xB | as a function of m and determine the value of m for which |xA ? xB | is the
shortest.

i decided to draw the graph of the function in which i realized that the distance of AB on the x axis would be the answer yet i am confused about how to use the slope. i think i may have confused myself.

 

[Deleted member 4993]

Consider a parabola with equation y = 4 ? x squared
and a point P : (a, b) in its interior. A line with slope m through P intersects the parabola at points A and B. Find
|xA ? xB | as a function of m and determine the value of m for which |xA ? xB | is the
shortest.

i decided to draw the graph of the function in which i realized that the distance of AB on the x axis would be the answer yet i am confused about how to use the slope. i think i may have confused myself.

Did you find the co-ordinates of A and B? What are those?