The longest distance of the point (a, 0) from the curve2x2+y2−2x=0 is given by

The longest distance of the point (a, 0) from the curve

2x2+y22x=0 is given by

  1. A

    12a+a2

  2. B

    1+2a+2a2

  3. C

    1+2aa2

  4. D

    12a+2a2

    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:

    Let (x, y) be the point on the curve 2x2+y22x=0

    Then its distance from (a, 0) is given by

    S=(xa)2+y2 S2=x22ax+a2+2x2x2  [Using 2x2+y22x=0 S2=x2+2x(1a)+a2 2SdSdx=2x+2(1a)

    For S to be maximum, we must have

    dSdx=02x+2(1a)=0x=1a

    It can be easily checked that d2Sdx2<0 for x=1a

    Hence, Sis maximum for x = 1 - a

    Putting x = l - a in (i), we get S=12a+2a2

    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.