5.34 A particle is placed at a point P on the parabola $y=x^{2}-x-6$ (the y-coordinate of P is 6), if the particle can freely roll along the parabola to point Q (the y-coordinate of Q is -6), then the shortest horizontal distance the particle moves is
(A) 5 .
(B) 4 .
(C) 3 .
(D) 2 .
(E) 1 .
(9th American High School Mathematics Examination, 1958)
[Solution] Suppose the coordinates of point $P$ are $(4,6)$ or $(-3,6)$; and the coordinates of point $Q$ are $(0,-6)$ or $(1,-6)$.

By symmetry and according to the problem, the particle rolls from $(4,6)$ to $(1,-6)$ or from $(-3,6)$ to $(0,-6)$.
The horizontal distance the particle moves is
$4-1=3$ or $0-(-3)=3$.
Therefore, the answer is $(C)$.