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Application Of Derivatives

Question
CBSEENMA12035240
Wired Faculty App

The normal at the point (1, 1) on the curve 2y + x2 = 3 is
  • x + y = 0
  • x – y = 0
  • x + y + 1 = 0
  • x – y = 2

Solution

B.

x – y = 0

The equation of curve is
                       2 straight y plus straight x squared space equals space 3
therefore space space space space space 2 dy over dx plus 2 straight x space equals space 0 space space space space space or space space space dy over dx space equals space minus straight x At space left parenthesis 1 comma space 1 right parenthesis comma space space space dy over dx space equals space minus 1 therefore space space space space slope space of space tangent space space equals negative 1 therefore space space space space space space space at space left parenthesis 1 comma space 1 right parenthesis comma space slope space of space normal space space equals space minus fraction numerator 1 over denominator negative 1 end fraction space equals space 1 therefore space space space space space space space equation space of space normal space at space left parenthesis 1 comma space 1 right parenthesis space is space space space space space space space space space space space space space space space space space space space space space space straight y minus 1 space equals 1 left parenthesis straight x minus 1 right parenthesis space space space space or space space space space space straight y minus 1 space equals space straight x minus 1 space space space or space space space straight x minus straight y space equals 0 therefore space space space left parenthesis straight B right parenthesis space is space correct space answer.

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