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 .

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 .

Multiply and .

Multiply by .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Rewrite as .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

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 .

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 .

Multiply and .

Multiply by .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Rewrite as .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

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 the numerator.

Multiply by .

Multiply by .

Simplify with factoring out.

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.

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 .

Simplify .

Simplify the numerator.

Multiply by .

Multiply by .

Simplify with factoring out.

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.

Rewrite as .

Multiply by .

Multiply by .

Simplify .

Simplify the numerator.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Simplify with factoring out.

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.

Rewrite as .

Multiply by .

Multiply by .

Simplify .

Simplify the numerator.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Simplify with factoring out.

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.

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