1. A curve is given in parametric equations: x = tan2 θ y = sec θ , 0 ≤ θ < π 2 . (a) Find a Cartesian equation for the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. (c) Find an equation for the tangent line to the curve at the point corresponding to θ = π 3 . 2. Find the points on the curve where the tangent is horizontal or vertical. x = t 3 − 3t y = t 3 − 3t 2 3. The following curve is called an astroid.