so u hav the equation of the tangent at P and at Q. you find the points of intersection and get co-ordinates for R.
well the coordinates of R are:
(3t, 2t^2)
t is your parameter (ur third variable). for the cartesian equation u want a relationship between x and y eliminating t.
so t = x/3
y = 2t^2
therefore y = 2(x/3)^2
y = 2x^2/9