Word Count : 308

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To find the differential equation of the family of curves given by: \[ x^2 + y^2 + 2ax + 2by + c = 0 \] where \(a\), \(b\), and \(c\) are parameters, we need to eliminate the parameters \(a\), \(b\), and \(c\) and derive a relationship involving \(x\), \(y\), and their derivatives. ### Step 1: Differentiate the given equation with respect to \(x\). Using implicit differentiation: \[ \frac{d}{dx}(x^2 + y^2 + 2ax + 2by + c) = _____ _____ _______ _________ _________ ____ ______ __________.
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