A tangent drawn to the curve [tex]y=f(x)[/tex] at [tex]P(x,y)[/tex] cuts the [tex]x[/tex] axis and [tex]y[/tex] axis at [tex]A[/tex] and [tex]B[/tex] respectively such that [tex]BP:AP=3:1[/tex]. Given that [tex]f(1)=1[/tex], which of the following is/are true?
A) The equation of the curve is [tex]x \frac{dy}{dx}-3y=0[\tex].
B) The normal at [tex](1,1)[\tex] is [tex]x+3y=4[\tex].
C) The curve passes through [tex](2, 1/8)[\tex].
D) The equation of the curve is [tex]x \frac{dy}{dx}+3y=0[\tex].​