A parabola is a symmetric, U-shaped curve that is defined as the set of all points in a plane equidistant from a fixed point called the focus and a fixed line called the directrix. Parabolas can be represented mathematically by quadratic equations in two variables, typically in the form of $$y = ax^2 + bx + c$$ or $$x = ay^2 + by + c$$. This unique shape is important in various applications, such as projectile motion and reflective properties in physics.
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