Montgomery Stuart

09/28/2023 · Junior High School

For a nonzero constant a, find the intercepts of the graph of \( \left(x^{2}+y^{2}\right)^{2}=a^{2}\left(x^{2}-y^{2}\right) \). Then test for symmetry with respect to the \( x \)-axis, the \( y \)-axis, and the origin. What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Use a comma to separate answers as needed. Type an ordered pair.) B. There are no intercepts. Test ( \( \left.x^{2}+y^{2}\right)^{2}=a^{2}\left(x^{2}-y^{2}\right) \) for symmetry with respect to the \( x \)-axis, the \( y \)-axis, and the origin. Select all that apply. A. The graph of the equation is symmetric with respect to the \( x \)-axis. B. The graph of the equaxtion is symmetric with respect to the \( y \)-axis. C. The graph of the equation is symmetric with respect to the origin. \( \square \) D. The graph of the equation is not symmetric.