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focal ratio theorem for conical curves

2025-01-10 12:26
2025-01-10 14:33

The focal ratio theorem of the conical curve was a theorem related to the polar coordinate equation of the conical curve. According to the given polar coordinate equation of the conical curve, p =ep/(1-e* cos0), and the straight line, 0 =c or 0 = Pi +c, where c is a constant, the focal ratio theorem can be derived as:| 1-e*cosc)/(1+e*cosc)|.The specific derivation process is as follows: Consider the intersection of the conical curve and the straight line. The coordinates of the intersection are (ep/(1-e*cosc), c) and (ep/(1+e*cosc), Pi +c). According to the definition of focal radius, the focal radius length was the distance from the focal point to the intersection point. Therefore, the ratio of focal radius to length is| 1-e*cosc)/(1+e*cosc)|.This was the derivation process of the focal ratio theorem for conical curves.

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