Show that for all values of t, the point P with the equation x=2t^2, y=t^3 lies on the curve 8y^2=x^3 Find the equation of the tangent to the curve at point P. The tangent meets the curve once again at point Q. Find the coordinates of point Q. I can find the equation of the tangent. After finding the tangent, I try to solve it by using the two equation. At the end I get 9t^2x^2-12t^4x+4t^6=2x^3. Is it the right way? It seems complicated.