question below
quimilar question You can retry this
Consider the curve given by the equation

What symmetries does this curve display? Check all that are
applicable.
symmetry about the -axis
symmetry about the -axis
symmetry about the origin
no symmetry

Ask by Boyd Schofield. in the United States

Mar 28,2025

Question

question below
quimilar question You can retry this
Consider the curve given by the equation

What symmetries does this curve display? Check all that are
applicable.
symmetry about the -axis
symmetry about the -axis
symmetry about the origin
no symmetry

Ask by Boyd Schofield. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

1. Replace $$x$$ by $$-x$$ (for symmetry about the $$y$$-axis):

The given equation is 
   $$
   2x^2 + 5y + 4y^2 = 74.
   $$
   Substituting $$-x$$ for $$x$$ gives:
   $$
   2(-x)^2 + 5y + 4y^2 = 2x^2 + 5y + 4y^2 = 74.
   $$
   Since the equation is unchanged, the curve is symmetric about the $$y$$-axis.

2. Replace $$y$$ by $$-y$$ (for symmetry about the $$x$$-axis):

Substituting $$-y$$ for $$y$$ gives:
   $$
   2x^2 + 5(-y) + 4(-y)^2 = 2x^2 - 5y + 4y^2 = 74.
   $$
   The resulting equation is not equivalent to the original equation for all $$(x, y)$$, so the curve is not symmetric about the $$x$$-axis.

3. Replace both $$x$$ by $$-x$$ and $$y$$ by $$-y$$ (for symmetry about the origin):

Substituting $$-x$$ for $$x$$ and $$-y$$ for $$y$$ gives:
   $$
   2(-x)^2 + 5(-y) + 4(-y)^2 = 2x^2 - 5y + 4y^2 = 74.
   $$
   Again, the resulting equation is not equivalent to the original equation for all $$(x, y)$$, so the curve is not symmetric about the origin.

Thus, the curve displays symmetry only about the $$y$$-axis.
The curve is symmetric about the $$y$$-axis.

question below
quimilar question You can retry this
Consider the curve given by the equation

What symmetries does this curve display? Check all that are
applicable.
symmetry about the -axis
symmetry about the -axis
symmetry about the origin
no symmetry

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question below quimilar question You can retry this Consider the curve given by the equation What symmetries does this curve display? Check all that are applicable. symmetry about the -axis symmetry about the -axis symmetry about the origin no symmetry

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question below
quimilar question You can retry this
Consider the curve given by the equation

What symmetries does this curve display? Check all that are
applicable.
symmetry about the -axis
symmetry about the -axis
symmetry about the origin
no symmetry