Chapter 10.2, Problem 64AYU

To determine

To find:

The location of the receiver is the placed at the focus

Answer to Problem 64AYU

  $a=1.125feet$

Explanation of Solution

Given:

The height

  $6feet$

Concept used:

The stabdard form of parabola equation

  $y=a{x}^2+bx+c$

Putting $x=h,y=k$ in equation (1)

  $k=a{h}^2+bh+c\mathrm{.......................}\left(2\right)$

Where $\left(h,k\right)$ is the vertex

Calculation:

The stabdard form of parabola equation

  $y=a{x}^2+bx+c$

Putting $x=h,y=k$ in equation (1)

  $\begin{array}{l}{x}^2=4ay\\ {\left(x-h\right)}^2=4a\left(y-k\right)\mathrm{.......................}\left(2\right)\end{array}$

Where $\left(h,k\right)$ is the vertex

  $\begin{array}{l}{x}^2=4ay\\ {\left(3\right)}^2=4a\left(2\right)\\ 9=8a\\ a=\frac{9}{8}feet\\ a=1.125feet\end{array}$