Find the Symmetry ((x-3)^2)/81-((y+5)^2)/16=1

Math
There are three types of symmetry:
1. X-Axis Symmetry
2. Y-Axis Symmetry
3. Origin Symmetry
If exists on the graph, then the graph is symmetric about the:
1. X-Axis if exists on the graph
2. Y-Axis if exists on the graph
3. Origin if exists on the graph
Check if the graph is symmetric about the x-axis by plugging in for .
Simplify .
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To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
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Apply the distributive property.
Move to the left of .
Multiply by .
Apply the distributive property.
Move to the left of .
Multiply by .
Add and .
Apply the distributive property.
Move to the left of .
Multiply by .
Apply the distributive property.
Move to the left of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Simplify .
Tap for more steps…
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Multiply and .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
Tap for more steps…
Apply the distributive property.
Move to the left of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Add and .
Apply the distributive property.
Move to the left of .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Since the equation is not identical to the original equation, it is not symmetric to the x-axis.
Not symmetric to the x-axis
Check if the graph is symmetric about the y-axis by plugging in for .
Simplify .
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Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Simplify with factoring out.
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Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
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Rewrite as .
Multiply by .
Multiply by .
Since the equation is not identical to the original equation, it is not symmetric to the y-axis.
Not symmetric to the y-axis
Check if the graph is symmetric about the origin by plugging in for and for .
Solve for .
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Simplify .
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Simplify with factoring out.
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Tap for more steps…
Rewrite as .
Multiply by .
Multiply by .
Simplify .
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify with factoring out.
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Tap for more steps…
Rewrite as .
Multiply by .
Multiply by .
Simplify .
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify with factoring out.
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Tap for more steps…
Rewrite as .
Multiply by .
Multiply by .
Multiply by .
Since the equation is not identical to the original equation, it is not symmetric to the origin.
Not symmetric to the origin
Determine the symmetry.
Not symmetric to the x-axis
Not symmetric to the y-axis
Not symmetric to the origin
Find the Symmetry ((x-3)^2)/81-((y+5)^2)/16=1

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