Assertion (A): The order of the differential | vedclass

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(A) The equation of a family of circles with a constant radius $a$ is given by $(x-h)^2 + (y-k)^2 = a^2$,where $(h, k)$ are the coordinates of the cen

Vedclass · Accepted Answer

$(A)$ and $(R)$ are true,$(R)$ is the correct explanation to $(A)$

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(A) The equation of a family of circles with a constant radius $a$ is given by $(x-h)^2 + (y-k)^2 = a^2$,where $(h, k)$ are the coordinates of the center.Here,$h$ and $k$ are two arbitrary constants.The order of the differential equation is equal to the number of arbitrary constants in the general solution.Since there are $2$ arbitrary constants,the order of the differential equation is $2$.Thus,Assertion $(A)$ is true.Furthermore,an algebraic equation with $2$ arbitrary constants represents the general solution of a second-order differential equation,making Reason $(R)$ true and the correct explanation for $(A)$.

Assertion $(A)$: The order of the differential equation of a family of circles with a constant radius is $2$.
Reason $(R)$: An algebraic equation having two arbitrary constants is the general solution of a second-order differential equation.

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Assertion $(A)$: The order of the differential equation of a family of circles with a constant radius is $2$.Reason $(R)$: An algebraic equation having two arbitrary constants is the general solution of a second-order differential equation.