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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

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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Regards,

7 years ago
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