1 given that y^2-5xy+8x^2=2, the distinct points P and Q on the curve each have x-coordinate 1.the normals to the curve at P and Q meet at the point N. Calculate the coordinates of N.

2. the points P(0,2) and Q lie on the curve y=x^2-3x+2. find the equation of the normal to the curve at each of the points P and Q. find the coordinates of R, the point where the normals meet.

3, find the fist 4 terms in the expansion of (1+3x)^1/3 in ascending powers of X and state the range of the values of x for which the expansion is valid. use the expansio nto determin (8*24)^1/3 to five decimal places.