A curve having the condition that the slope of tangent at some ponits is two times the slope of straight line joining the same point to the origin of coordinates is a

Dear  pallavi

let the curve is y=f(x)

any point on the curve is (x,f(x))

 slope of tangent at this point is  = f'(x)

slope of line joinnig by origin and (x,f(x) is  = f(x) -0 /x -0

                                                              =f(x) /x

  so given  f'(x) = 2f(x) /x   .....................1

             f'(x) /f(x)  = 2/x

           ∫ f'(x) /f(x)   dx   =  ∫2/x  dx

           lnf(x)   = 2 lnx  +lnC

                      =lnCx²

            f(x)  = CX²

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