Test algebraically whether it is symmetric with respect to the x axis the y axis, and the origin. Then check your work graphically, if possible. a. 3x? – 2y? = 3 b. xy – x² = 3 с. уз 3 2x?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Test algebraically whether it is symmetric with respect to the x-axis the y axis, and the origin. Then check your work graphically, if possible.

20. Test algebraically whether it is symmetric with respect to the x axis the y axis,
and the origin. Then check your work graphically, if possible.
а. Зx2 — 2у2 — 3
b. ху — х? %3D 3
c. y = 2x?
Transcribed Image Text:20. Test algebraically whether it is symmetric with respect to the x axis the y axis, and the origin. Then check your work graphically, if possible. а. Зx2 — 2у2 — 3 b. ху — х? %3D 3 c. y = 2x?
Expert Solution
Step 1

Algebraic tests for symmetry:

  • A graph will have symmetry about the x-axis if we get the same equation when all y's are replaced by -y.
  • A graph will have symmetry about the y-axis if we get the same equation when all x's are replaced by -x.
  • A graph will have symmetry about the origin if we get the same equation when all y's are replaced by -y and all x's are replaced by -x.

 

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