Question

perform the symmetry test for following: -x^2 + y^2 = 1

Answer 1

Answer:

The equation is symmetric with respect to the x-axis, y-axis, and the origin.

Explanation:

To find symmetry with respect to the x-axis, we replace y by -y and see if the equation remains the same.

$\begin{gathered} -x^2+(-y)^2=1 \\ -x^2+y^2=1 \end{gathered}$

The equation remains the same, and is symmetric with respect to the x-axis

With respect to the y-axis, we replace x by -x

$\begin{gathered} -(-x)^2+y^2=1 \\ -x^2+y^2=1 \end{gathered}$

The equation is symmetric with respect to the y-axis

With respect to the origin, we replace x by -x and y by -y and see if the equation remains the same

$\begin{gathered} -(-x^2)+(-y)^2=1 \\ -x^2+y^2=1 \end{gathered}$

The equation remains the same and is symmetric.