Question

A lithotripter is device to break kidney stone by propagating shock waves through water in elliptical chamber.High frequency sound waves are generated at one focus they reflect through the boundry of ellitical chamber and hit the other focus. The patient is so adjusted that the kidney stone is positioned at other focus. Find the positions of shock wave generator and the stone if vertex is (6,0) and one end of minor axis is at (0,-3)

Answer 1

if shock wave generator is at S', patient's kidney stone should be at S.

for above ellipse,

a = 6

b = 3

$e=\sqrt{1-\frac{{\left(3\right)}^2}{{\left(6\right)}^2}}\Rightarrow e=\sqrt{1-\frac{9}{36}}\Rightarrow e=\sqrt{\frac{27}{36}}$

ae = $6\times \frac{\sqrt{27}}{6}\Rightarrow 3\sqrt{3}$

$⨀$ if shockwave generator is at $(-3\sqrt{3},0)$, patient should be at $(3\sqrt{3},0)$

$⨀$ if shockwave generator is at $(3\sqrt{3},0)$, patient should be at $(-3\sqrt{3},0)$.