Answer
The graph of the given equation is symmetric with respect to the x-axis, y-axis, and origin.
Work Step by Step
Replace y with -y in the equation x² + 4y² = 16.
x² + 4(-y)² = 16
x² + 4y² = 16, which is equivalent to the given equation.
Hence the graph is symmetric with respect to the x-axis.
Replace x with –x.
(-x)² + 4y² = 16
x² + 4y² = 16, which is equivalent to the given equation.
Hence the graph is symmetric with respect to the y-axis.
Replace x with -x and y with –y.
(-x)² + 4(-y)² = 16
x² + 4y² = 16, which is equivalent to the given equation.
Hence the graph is symmetric with respect to the origin.
