Question

Without graphing, determine whether the following equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.x² + y² = 16Select all that apply.A. y-axisB. originC. x-axisD. none of these

Answer 1

Given,

The equation of the graph is,

$x^{2}+y^{2}=16$

By replacing x by -x, if the equation remain the same then it is symmetric about the x axis.

$\begin{gathered} (-x)^2+y^2=16 \\ x^2+y^2=16 \end{gathered}$

Hence, the equation is symmetric about x axis.

By replacing y by -y, if the equation remain the same then it is symmetric about the y axis.

$\begin{gathered} (x)^2+(-y)^2=16 \\ x^2+y^2=16 \end{gathered}$

Hence, the equation is symmetric about y axis.

The equation is symmetric about the origin.

Hence, The equation is symmetric about x- axis, y-axis and origin.