Find the Orthogonal Trajectories of the Family of Curves $y = ( x + k ) ^ { - 8 }$

question 65

Short Answer

Find the orthogonal trajectories of the family of curves. $y = ( x + k ) ^ { - 8 }$

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Definitions:

Religious Fanaticism

Extreme and uncritical zeal or enthusiasm related to religious beliefs, often leading to intolerance or aggression towards others.

Powerful

Having great power, influence, or effect over others or situations, often associated with possession of physical strength, wealth, or position in society.

Social Rule

A guideline, expectation, or norm that governs behavior within a society, helping to maintain order and facilitate interactions among its members.

Humanities

Academic disciplines that study human culture, including literature, history, art, music, and philosophy.