Question

A lithotripter of height 15 cm and diameter 18 cm is to be constructed from a semi-ellipse. High energy underwater shock waves will be emitted from the focus that is closest to the vertex V in order to break down the kidney stone. How far from V in the vertical direction should a kidney stone be located to receive the greatest effect of the shock waves?

Answer 1

27 cm

Explanation:

You want the distance from the vertex of an ellipse to the opposite focus if the semi-major axis is 15 cm, and the minor axis is 18 cm.

Center to focus

The square of the distance from the center to either focus is the difference of the squares of the semi-axes. The semi-minor axis is half the diameter of the ellipsoid.

c² = 15² -(18/2)² = 225 -81 = 144

c = √144 = 12 . . . . . cm

Vertex to focus

The distance from the vertex (V) to the opposite focus is the distance from vertex to center plus the distance from center to focus:

15 cm +12 cm = 27 cm

The kidney stone should be located 27 cm from the vertex for greatest effect.