3 pts Let \( x^{2}+y^{2}=1 \) an equation. 1. This equation represents a \( \square \) [Select] 2. The graph of this equation has \( \square \) [Select] \( x \)-intercepts. 3. The graph of this equation has \( \square \) [Select] \( y \)-intercepts.

This equation represents a circle centered at the origin with a radius of 1. Circles are fascinating shapes that have been studied for centuries, and they pop up in art, architecture, and nature, from the orbits of planets to the petals of flowers! The graph of this equation has two \( x \)-intercepts: \( (1, 0) \) and \( (-1, 0) \). These points are where the circle touches the \( x \)-axis, showcasing the perfect symmetry of a circle. You can envision these points as the tips of a hula hoop lying flat on the ground! The graph of this equation has two \( y \)-intercepts as well: \( (0, 1) \) and \( (0, -1) \). Just like the \( x \)-intercepts, these points highlight the circle's wonderful symmetry, enveloping the coordinates in a dance around the origin. If you were to plot them, you’d create a lovely game of connect-the-dots!