Two curves are orthogonal if their tangent lines areperpendicular at each point of intersection. Show that the givenfamilies of curves are orthogonal trajectories of each other,that is, every curve in one family is orthogonal to every curvein the other family. Sketch both families of curves on the same axes.  y = ax 3 ,     x 2+ 3 y 2   =  b

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Two curves are orthogonal if their tangent lines are
perpendicular at each point of intersection. Show that the given
families of curves are orthogonal trajectories of each other,
that is, every curve in one family is orthogonal to every curve
in the other family. Sketch both families of curves on the same axes. 

y = ax 3 ,     x 2+ 3 y 2   =  b

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