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Find the differential equation of the family of circles passing through the origin and having their centres on the x -axis.

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Find the differential equation of the family of circles passing through the origin and having their centres on the x -axis.

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All circles passing through the origin and having their centre on the x -axis say at (a, 0) will have radius ‘a’ units. 

∴ Equation of circle is (x – a ) + y = a ... (1) [∵ ‘a’ arbitrary constant] 

Differentiate with respect to ‘x’

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