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  4. If the order of the differential equation of the family of circles touching the x -axis at the origin is k , then 2k is equal to

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Q. If the order of the differential equation of the family of circles touching the $x$ -axis at the origin is $k$ , then $2k$ is equal to

NTA AbhyasNTA Abhyas 2020Differential Equations

Solution:

Solution
The equation of the family is $x^{2}+\left(y - r\right)^{2}=r^{2}$
i.e. only one arbitrary constant.
Hence, the order of its differential equation will be $'1'$
$\therefore 2k=2$