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pallavi pradeep bhardwaj Grade: 12
        

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

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin

7 years ago
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