Consider the family of curves x = ky² A. Please draw 3-4 curves that belong to this family of curves? What shapes do these curves take? B. What is the definition of orthogonal? C. What is the definition of orthogonal trajectories? D. Using the definition of orthogonal and orthogonal trajectories, explain, in your own words, why we need to first find the derivative of the given family of functions if we want to find their orthogonal trajectories. E. Please find the orthogonal trajectories for the given family of curves? F. What shapes do these curves take? Please graph both the given family of curves and the orthogonal trajectories on the same graph.

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