Chapter 9.3, Problem 37WE

To determine

To explain: The reason for the sum $FP+PQ$ remains same for all positions of P.

Explanation of Solution

Given information: F is the focus point and line L is parallel to the directrix D.

Proof: As the graph is a parabola with directrix D and focus F,

  $PF=FD$

Then,

  $\begin{array}{l}\Rightarrow FP+PQ=FP+\left(DQ-PD\right)\\ =\left(FP-PD\right)+DQ\\ =0+DQ\\ =DQ\end{array}$

As Q parallel to D and the distance DQ is going to be constant.

Therefore, $FP+PQ=\mathrm{constant}$

Hence, proved.