Calculus AB Independent Study Conic Sections Study Sheet 3. Consider the curve generated by the equation y2 = x3(2 -x), depicted below. This classic curve is called the piriform. Find the points on the piriform where the tangent is horizontal. 4. Two curves are called orthogonal if at each point of intersection their tangent lines are perpendicular. Show that the two curves xy = c and x2 -y2 = k are orthogonal, for any constants c # 0 and k # 0. 5. Consider the curve defined by x2 + xy + 12 = 27. A. Write an expression for the slope d of the curve at any point (x, y). B. Determine whether the lines tangent to the curve at the x-intercepts of the curve are parallel. Show the analysis that leads to your conclusion. C. Find the points on the curve where the lines tangent to the curve are vertical