Find the envelope and the characteristic curves of the family of curves:

c and αare constants. 

To find the envelope and characteristic curves of the given family of curves, let's analyze the equation:

\[x^{2}(y-c)^{2} + z^{2} = c^{2} \cos^{2}\alpha\]

This equation represents a family of surfaces in three dimensions parameterized by \(c\) and \(\alpha\). To find the envelope of this family of surfaces, we need to find the conditions under which all members of the family are tangent to the same surface.

To find the envelope, we differentiate the equation of the family of surfaces with respect _________ __________ __________ ________ ___ ________ _______ ________.
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