Problem 51E

49-52 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.

51. $y=c x^{2}, \quad x^{2}+2 y^{2}=k$


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