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Form a differential equation for the family of curves represented by `ax^2 + by^2 = 1`, where a and b are arbitrary constants.
A. second order and second degree
B. first order and second degree
C. first order and first degree
D. second order and first degree

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Correct Answer - D
We have,
`Ax^(2)+By^(2)=1" …(i)"`
Differentiating w.r. to x, we get
`2Ax+2By(dy)/(dx)=0 rArr Ax +By(dy)/(dx)=0" …(ii)"`
Differentiating w.r. to x, we get
`A+B((dy)/(dx))^(2)+By(d^(2)y)/(dx^(2))=0" …(iii)"`
Multiplying (iii) by x and subtracting (ii) from it, we get
`x((dy)/(dx))^(2)+xy(d^(2)y)/(dx^(2))-y(dy)/(dx)=0`
Clearly, it is a second order and first degree differential equation.

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