Identifying surfaces Consider the surfaces defined by the following equations. a. Identify and briefly describe the surface. b. Find the xy-, xz-, and yz-traces, when they exist. c. Find the intercepts with the three coordinate axes, when they exist. d. Make a sketch of the surface. 18. x = y 2 64 − z 2 9
Identifying surfaces Consider the surfaces defined by the following equations. a. Identify and briefly describe the surface. b. Find the xy-, xz-, and yz-traces, when they exist. c. Find the intercepts with the three coordinate axes, when they exist. d. Make a sketch of the surface. 18. x = y 2 64 − z 2 9
Solution Summary: The author explains that the given equation is a hyperbolic paraboloid.
Identify and sketch the surfaces described by the given equations. Explain.
Consider the following equation of a quadric surface.
y²
25
100
+
= z²
a. Find the intercepts with the three coordinate axes, if they exist.
b. Find the equations of the xy-, xz-, and yz-traces, if they exist.
c. Identify and sketch a graph of the surface.
a. Find the x-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice.
A. The surface intersects the x-axis at x =
(Use a comma to separate answers as needed.)
B. There are no x-intercepts.
.2
x + 20x + y + 16y = -20
The equation above defines a circle in the xy-plane.
What are the coordinates of the center of the circle?
A) (-20,–16)
|
B) (-10,–8)
C) (10,8)
D) (20,16)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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