A tangent to the curve, y = f(x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point :

The tangent at the point (2, $$-$$2) to the curve, x²y² $$-$$ 2x = 4(1 $$-$$ y) does not pass through the point :

Let C be a curve given by y(x) = 1 + $$\sqrt {4x - 3} ,x > {3 \over 4}.$$ If P is a point on C, such that the tangent at P has slope $${2 \over 3}$$, then a point through which the normal at P passes, is :

If the tangent at a point P, with parameter t, on the curve x = 4t² + 3, y = 8t³−1, t $$ \in $$ R, meets the curve again at a point Q, then the coordinates of Q are :