Tangent is drawn at any point \(P(x, y)\) on a curve, which passes through \((1,1)\). The tangent cuts \(X\)-axis and \(Y\)-axis at \(A\) and \(B\) respectively. If \(A P: B P=3: 1\), then
(A) the differential equation of the curve is \(3 x \frac{d y}{d x}+y=0\)
(B) the differential equation of the curve is \(3 x \frac{d y}{d x}-y=0\)
(C) the curve passes through \(\left(\frac{1}{8}, 2\right)\)
(D) the normal at \((1,1)\) is \(x+3 y=4\)
Ans: (A,C)
