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

question 11

Essay

Find the orthogonal trajectories of the family of curves $y = k x ^ { 2 }$ . Then draw several members of each family on the same coordinate plane.

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Definitions:

Sample Size

The number of observations or data points collected in a sample from the larger population for the purpose of statistical analysis.

Nonparametric Methods

Statistical methods that do not rely on data belonging to any particular distribution, often used when data doesn't meet the assumptions required for parametric testing.

Parametric Methods

Statistical methods that assume the data samples have a specific distribution.

Rigid Requirements

Strict, inflexible criteria or conditions that must be met or adhered to.