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A planetary nebula can be identified by the following two characteristics:
1. **Spherical shape** - Planetary nebulae often exhibit a roughly spherical appearance as they expand in all directions.
2. **Central star remnant** - They typically contain a central star remnant, which is a hot core of gas that is often shining brightly as it emits ultraviolet radiation.
So, the correct answers are "spherical shape" and "central star remnant."