To calculate : An equation for the cross section of the ellipsoid with the given dimensions and the distance between the foci.
The equation for the cross section of the ellipsoid is
Given information :
A lithotripter uses shock waves to break apart kidney stones or gallstones inside the body. Shock waves generated at one focus of an ellipsoid (a three-dimensional shape with an elliptical cross section) reflect to the stone positioned at the second focus.
Formula used:
The standard equation of an ellipse with horizontal major axis is,
Calculation :
Draw the figure as below:
Since major axis is horizontal. Standard equation of an ellipse with major axis is
The length of the major axis is
The length of the minor axis is
Write the equation of ellipse.
The coordinates of the foci will be:
The eccentricity
So, the coordinates of the foci will be,
Distance between
Therefore, the equation for the cross section of the ellipsoid is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education