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MHT CET202519 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The equation of tangent to the curve y = (x+ y ) where -2 x 2 and which is parallel to the line x+2 y =0 , is

Options

  1. A2 x+4 y+ =0
  2. B2 x+4 y- =0
  3. C2 x+4 y-3 =0
  4. D2 x-4 y+3 =0

Correct answer

B. 2 x+4 y- =0

Step-by-step solution

The tangent to y = (x + y) parallel to x + 2y = 0 must share the line's slope, which by rearrangement to y = - 1 2 x is m = - 1 2 . Implicit differentiation of the curve yields: dy dx = - (x + y) (1 + dy dx ) Solving for dy dx gives: dy dx = - (x + y) 1 + (x + y) Equating this to - 1 2 and simplifying leads to (x + y) = 1 , which implies x + y = 2 + 2n for integer n . Substituting into the original equation and using (x + y) = 0 gives y = 0 , so x = 2 + 2n . Within -2 x 2 , valid points are ( 2 , 0 ) and (- 3 2 , 0

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