If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:

Option 1 -

0

Option 2 -

-t3

Option 3 -

-2t3

Option 4 -

2t3

0 2 Views | Posted 2 weeks ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    2 weeks ago
    Correct Option - 3


    Detailed Solution:

    y = x3

    d y d x = 3 x 2 d y d x | ( t , t 3 ) = 3 t 2

    Equation of tangent y – t3 = 3t2 (x – t) 

    Let again meet the curve at Q ( t 1 , t 1 3 )

    t 1 3 t 3 = 3 t 2 ( t 1 t )

    t 1 2 + t t 1 + t 2 = 3 t 2 [ ? t 1 t ]

    t 1 2 + t t 1 2 t 2 = 0

    => t1 = -2t

    Required ordinate = 2 t 3 + t 1 3 3 = 2 t 3 8 t 3 3 = 2 t 3   

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V
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