Chapter 2, Problem 9CR

To determine

To find: The distance between wire from bottom.

Answer to Problem 9CR

The wire should be placed $2.25$ inches from the bottom.

Explanation of Solution

Given information: A parabola with $12$ inches width and $4$ inches depth.

The formula for a parabola that has $12$ inches width and $4$ inches depth is,

  $y=a{x}^2$

Substituting $(6,4)$ in the above equation, we get

  $\begin{array}{c}4=a\times 6^2\\ 4=a\times 36\\ a=\frac{4}{36}\\ a=\frac{1}{9}\end{array}$

The focus point of the parabola is,

  $\begin{array}{c}f=\frac{1}{4a}\\ f=\frac{1}{4\times \frac{1}{9}}\\ f=\frac{1}{4}\times \frac{9}{1}\\ f=\frac{9}{4}\\ f=2.25\text{in}\end{array}$

Therefore, we can conclude that the wire should be places $2.25$ from the bottom.