Word Count : 327

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To find the envelope and the characteristic curves of the family of curves defined by the equation: \[ x^{2}(y-c)^{2}+z^{2}=c^{2}\, \cos^{2} \, \alpha, \] where \(c\) and \(\alpha\) are constants, we can proceed step-by-step. ### Step 1: Implicit Differentiation The general method to find the envelope is to first find the partial derivatives with respect to the parameter \(c\) (since \(c\) is a constant) and set them equal to zero. We begin by implicitly differentiating the equation with respect to \(c\). The _________ _______ ___ ______ _________ _____ ________ ___ _________ _________.
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