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in the above question i m geting ans D but the ans js B plz expalin me

in the above question i m geting ans D but the ans js B plz expalin me 

Question Image
Grade:12th pass

1 Answers

Susmita
425 Points
2 years ago
Given  x=\phi (t) and y=\psi (t)
Differentiate with respect  to t.
\frac{dx}{dt} = \phi ` (t) and \frac{dy}{dt} = \psi ` (t)
Now \frac{dy}{dx} = \frac{dy}{dt} \frac{dt}{dx} =\frac{\psi `}{\phi `} 
\frac{d^2 y}{dx^2} =\frac{d}{dx}( \frac{dy}{dx})
          =\frac{d}{dt} (\frac{dy}{dx} ) \frac{dt}{dx}
          =\frac{d}{dt} (\frac{\psi `}{\phi `} ) \frac{1}{\phi `}
            =(\frac{\phi ` \psi `` - \psi ` \phi ``}{\phi `^2} ) \frac{1}{\phi `}
So the ans is b.Please approve the answer if you are helped.
          

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