In relation to a parabola (and more generally, any conic section), a polar is a line that has a special reciprocal relationship with a point called the pole. This relationship is defined with respect to the conic section.
Here's a breakdown:
- Pole: A specific point related to the conic section.
- Polar: A line uniquely associated with the pole.
According to the provided reference, "In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section."
While the reference talks about the general case of conic sections, the same principle applies to parabolas specifically. The polar of a point Q with respect to a parabola is a line q. If you know the coordinates of the point Q, you can determine the equation of the polar line q. Similarly, if you know the equation of the polar line q, you can determine the coordinates of the pole Q.
