Chapter 8.2, Problem 60E

Solution

The position of the shockwave source and the patient, for maximum effect.

It has been determined that for maximum effect, the shockwave source and the patient should each be placed at a distance $12$ inches from the center on opposite sides, on the major axis.

Given:

A lithotripter’s shape is formed by rotating the portion of an ellipse below its minor axis about its major axis. The length of the major axis is $26$ inches and the length of the minor axis is $10$ inches.

Concept used:

If an ellipse has semi-major axis $a$ and semi-minor axis $b$ , then the foci are at a distance of $c$ from the center on the major axis, where $c^2=a^2-b^2$ .

Calculation:

It is given that the length of the major axis is $26$ inches.

Then, the length of the semi-major axis is given as $a=\frac{26}{2}=13$ inches.

It is given that the length of the minor axis is $10$ inches.

Then, the length of the semi-minor axis is given as $b=\frac{10}{2}=5$ inches.

Put $a=13$ and $b=5$ in $c^2=a^2-b^2$ to get,

  $\begin{array}{c}{c}^2={\left(13\right)}^2-{\left(5\right)}^2\\ =169-25\\ =144\end{array}$

Solving,

  $c=\pm 12$

This implies that for maximum effect, the shockwave source and the patient should each be placed at a distance $12$ inches from the center on opposite sides, on the major axis.

Conclusion:

It has been determined that for maximum effect, the shockwave source and the patient should each be placed at a distance $12$ inches from the center on opposite sides, on the major axis.