Find the Orthogonal Trajectories of the Family of Curves $$k x ^ { 2 } + y ^ { 2 } = 1$$

question 73

Essay

Find the orthogonal trajectories of the family of curves. Sketch several members of each family.
- $$k x ^ { 2 } + y ^ { 2 } = 1$$

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Definitions:

Turner Syndrome

A genetic disorder affecting females, characterized by the complete or partial absence of one of the X chromosomes, leading to developmental abnormalities and infertility.

Sense-Pleasure

Enjoyment or satisfaction derived from sensory experiences, such as tastes, smells, and tactile sensations.

Turner Syndrome

A chromosomal disorder affecting females, where one of the X chromosomes is missing or partially missing, leading to developmental and reproductive issues.

X Chromosome

One of the two sex chromosomes, which in humans and most animals determines the sex of the individual; females have two X chromosomes, males one X and one Y chromosome.