please answer the questions in handwritten form

1a) Show that the parametric curve given by x = t^2 + 1, y = t^3 - 2t intersects itself at the point (x,y) = (3,0) by finding two different values of t that give this point on the curve. 1b) Find the equations of the two tangent lines to the curve at this point. 1c) Identify coordinates of points on the curve with (i) a horizontal tangent (ii) a vertical tangent. 1d) Sketch the curve showing its orientation.