Word Count : 409

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To find the differential equation of the space curve defined by the intersection of the two families of surfaces, we need to first describe the surfaces in terms of their equations: The given surfaces are: 1. \( u = x^2 - y^2 = c_1 \) 2. \( v = y^2 - z^2 = c_2 \) Where \( c_1 \) and \( c_2 \) are constants. ### Step 1: Parameterize the curves We will now express the variables \( x \), \( _________ __________ ______ ______ ___ ____ ___ __________.
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