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Given the quadratic surface: x^2 + z^2 + 4y = 0. Describe the traces of the quadratic surface and...

Question:

Given the quadratic surface: {eq}x^2 + z^2 - 4y = 0 {/eq}

Describe the traces of the quadratic surface and sketch.

Circular Paraboloid:


This is one of the six basic surfaces of three-dimensional space, with the exception that its trace concerning the parallel plane {eq}xy {/eq} does not form an ellipse, but circles or circumference, hence it is not called elliptical but circular paraboloid.

Answer and Explanation: 1

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Let {eq}x^2 + y^2 -4z = 0 \to 4z = x^2 + y^2 \to z= \dfrac{x^2}{4} + \dfrac{y^2}{4}. {/eq}

This represents an elliptical paraboloid, whose traces...

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Practice Problems with Circular Trigonometric Functions

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Chapter 16 / Lesson 5
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Circular trigonometric functions are the trig functions which are calculated using a circle. Learn more about the unit circle, degrees, and radians, and apply your understanding by working through example problems.


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