Solve the Problem $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } = 1$

question 150

Essay

Solve the problem.
-Find a parametrization for the ellipsoid $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } = 1$ . (Recall that the parametrization of an ellipse $\frac { x ^ { 2 } } { 36 } +$ $\frac { y ^ { 2 } } { 81 } = 1$ is $\left. x = 6 \cos \theta , y = 9 \sin \theta , 0 \leq \theta < 2 \pi \right)$

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Definitions:

Intercostal Space

The anatomical area between two ribs, containing muscles and nerves, significant in respiratory function.

Midclavicular Line

Midclavicular Line is an imaginary line drawn vertically through the midpoint of the clavicle, commonly used as a reference in physical examination and medical imaging.

Thrill

A sudden feeling of excitement and pleasure or, in a medical context, a vibration felt on palpation, indicative of an abnormal blood flow or heart murmur.

Pedal Pulses

The palpable beats felt over the foot's arteries, reflecting the circulation to the lower extremities.