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If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is x 2 − 4 x + y + 8 x − 2 , then this curve also passes through the point:

Option 1 -

(5, 5)

Option 2 -

(4, 4)

Option 3 -

(4, 5)

Option 4 -

(5, 4)

0 2 Views | Posted a month ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    a month ago
    Correct Option - 1


    Detailed Solution:

    As per questions

    d y d x = x 2 − 4 x + y + 8 x − 2           

    d y d x = ( x − 2 ) 2 + ( y + 4 ) ( x − 2 )           

    d y d x = ( x − 2 ) + y + 4 x − 2                       .(i)

    Let y + 4 x − 2 = t  

    (y + 4) = t(x – 2)

    Putting in equation (i)

    ( x − 2 ) d t d x + t = ( x − 2 ) + t        

        d t d x = 1        

    dt = dx

    Integrating on both the sides t = x + c

    y + 4 x − 2 = x + c  

    Passing through origin C = -2

      ∴         equation of curve y + 4 x − 2 = x − 2

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