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KCET2023MathematicsApplication of Derivatives

A particle moves along the curve x^2 16 + y^2 4 =1 . When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

Options

  1. AII or IV
  2. BIII or IV
  3. CII or III
  4. DI or III

Correct answer

D. I or III

Step-by-step solution

Given, particles moves along the curve x^2 16 + y^2 4 = 2 x 16 + 2 y 4 d y d x =0 d y d x = -2 x 16 4 2 y = -x 4 y According to the question, x=4 y From Eq. (i), we get d y d x =-1 When slope is negative, then the particle lies in Ist and IIIrd quadrant.

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