Hello!
The equation is
The central (point) symmetry with respect to the origin moves a point with the coordinates (x, y) to the point (-x, -y). If a point (x_1, y_1) satisfies the equation, i.e.
then its image satisfies it, too:
This means that this graph has central symmetry and its center of symmetry is the point (0, 0).
The same idea works for the line (reflection) symmetry. Reflection over the x-axis moves (x, y) to (x, -y), and if
then also
Similarly the reflection over the y-axis moves (x, y) to (-x, y) and it is also a symmetry of this graph.
The answer: yes, this graph has line symmetry with respect to the x-axis, and with respect to the y-axis, and it has point symmetry with respect to the origin.
This graph (ellipse, actually) has no more axes of symmetry.
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