The order of the differential equation of all circles of a given radius a is.

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Solution

$The equation of a circle of radius a and any arbitary center is {(x - h)}^{2} + {(y - k)}^{2} = a^{2} Here although we see 3 constants h, k and a, a is a fixed constant and the order of the DE is given by the number of arbitary constants . The question might as well have asked about the order of DE of the family of circles having radius 5 . The equation in that case will be {(x - h)}^{2} + {(y - k)}^{2} = 25 . It is clearer to see from this why the order is 2 and not 3 .$

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