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COMEDK2014MathematicsApplication of Derivatives

The curve x²-x y+y²=27 has tangents parallel to X -axis at

Options

  1. A(-3,-6) and (3,-6)
  2. B(3,6) and (-3,-6)
  3. C(-3,6) and (-3,-6)
  4. D(3,-6) and (-3,6)

Correct answer

B. (3,6) and (-3,-6)

Step-by-step solution

Given, equation of curve is x²-x y+y²=27 ...(i) Taking derivative w.r.t. x on both sides gathered 2 x- x d y d x -y+2 y d y d x =0 d y d x (2 y-x)=y-2 x d y d x = y-2 x 2 y-x gathered Since, curve has tangent parallel to X -axis. Slope of tangent =0 array ll & d y d x =0 y-2 x 2 y-x =0 & y=2 x ...(ii) array Now, solving Eqs. (i) and (ii), we get x²-2 x²+4 x²=27 3 x²=27 x= 3 For x=3, y=6 and x=-3, y=-6 Points are (3,6) and (-3,-6) .

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