Assertion (A) Order of the differential equations of a family of circles with constant radius is two. Reason…
Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.
$(\mathrm{A})$ and $(\mathrm{R})$ are true, $(\mathrm{R})$ is the correct explanation to $(A)$
$(A)$ is true, $(R)$ is false
(A) and (R) are false, $(R)$ is not the correct explanation to $(A)$
$(A)$ is false, $(R)$ is true
Solution
Any circle with given radius can be written as, $(x-h)^2+(y-k)^2=a^2$ where $(h, k)$ be the centre of the circle which is variable. So, in above algebraic equation, there are two arbitrary constant $h$ and $k$. Hence, order of differential equation will be second order.
Hence, assertion and reason are true and reason is the correct explanation to assertion.