AP EAMCET · Maths · Differential Equations
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.
- A \((\mathrm{A})\) and \((\mathrm{R})\) are true, \((\mathrm{R})\) is the correct explanation to \((A)\)
- B \((A)\) is true, \((R)\) is false
- C (A) and (R) are false, \((R)\) is not the correct explanation to \((A)\)
- D \((A)\) is false, \((R)\) is true
Answer & Solution
Correct Answer
(A) \((\mathrm{A})\) and \((\mathrm{R})\) are true, \((\mathrm{R})\) is the correct explanation to \((A)\)
Step-by-step Solution
Detailed explanation
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.…
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