IGNOU MTE 8 2018 - Find the differential equation of the family of curves x2 + y2 + 2ax +

Question

Find the differential equation of the family of curves x² + y²+ 2ax + 2by + c = 0 , where a,b,c, are parameters.

13 Feb 2018

Answer :

Word Count : 265

To find the differential equation of the given family of curves \( x^2 + y^2 + 2ax + 2by + c = 0 \), where \( a \), \( b \), and \( c \) are parameters, we need to eliminate these parameters. ### Steps: 1. Differentiate the equation implicitly with respect to \( x \): \[ \frac{d}{dx}(x^2 + y^2 + 2ax + 2by + c) = 0 \] Applying the differentiation rule: \[ 2x + 2y \frac{dy}{dx} + 2a + 2b \frac{dy}{dx} = 0 \] 2. Simplify the equation: \[ 2x + 2a + \left( 2y + 2b \right) \frac{dy}{dx}

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