Question
Asked Sep 14, 2019
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a. What is the family of orthogonal trajectories for the family of parabolas with axis parallel to the y-axis and vertex at the point (−2, 4)?

b. Give the family of orthogonal trajectories of the family of parabolas with vertical axis and vertex at the point ( -6 , -4 ).

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Expert Answer

Step 1

To determine the equations of the families of orthogonal trajectories for the given families of parabolas

Step 2

By definition, every member of the orthogonal family meets every member of the given family orthognally. That is, the tangents at the points of intersections are perpendicular. 

Step 3
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a)The family of parabolas with vertex at (-2,4), and axis parallel to y-axis: (y-4)a(x+2) slope = y' 2a(x+2)

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