Write in standard form and identify the surface. Use at least two traces and sketch. Label the interesting points and try to be neat: 6x2+y+24z2=0
Write in standard form and identify the surface. Use at least two traces and sketch. Label the interesting points and try to be neat: 6x2+y+24z2=0
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.6: Surface Areas Of Pyramids And Cones
Problem 15E
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Question
Write in standard form and identify the surface. Use at least two traces and sketch. Label the interesting points and try to be neat:
6x2+y+24z2=0
Expert Solution
Step 1
Given,
The surface,
Step 2
Consider the given quadratic surface,
It can be rewritten as,
The standard form of Elliptic paraboloid is .
Thus, the given quadratic surface is elliptical paraboloid.
Step 3
Consider, the given surface
The parabola opens along the variable with degree 1 and its coefficient gives the direction.
Here, parabola is opens along y axis with -1/6 coefficient, so it is along negative y axis.
Set x= 0, gives
This is the parabola along negative y axis.
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