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 =cx2 ,  x2+ 2y2 =k

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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 =cx2 ,  x2+ 2y2 =k

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