The coordinates of the point on the ellipse 16×2+9y2=400 where the ordinate decreases at the same rate at which the abscissa increases, are

The coordinates of the point on the ellipse 16x2+9y2=400 where the ordinate decreases at the same rate at which the abscissa increases, are

  1. A

    (3 , 16/3) 

  2. B

    (-3 , 16/3)

  3. C

    (3 ,-16/3) 

  4. D

     (3 ,-3)

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    We have, 

              16x2+9y2=400 32xdxdt+18ydydt=0                                [Differentiating w.r.t. t] 

     32xdxdt18ydxdt=0                                 dydt=dxdt (given) 

     16x9y=0 y=16x9

     16x2+9y2=40016x2+2569x2=400x=±3

    Now y=169x and x=±3y=±163

    Hence , the required points are (3 ,16/3) and (-3 ,-16/3)

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.