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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
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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