1. Find the intersection points of the following pairs of objects. (Where you have square roots. you can leave your answers in square root form you don't need to evaluate to demical approximations.) (20) a. The line y = 4m 6 and the parabola y = 2a:2 + 4x + 4. b. The circle :32 + (y 3)2 = 9 and parabola y = :4; (Hint: Ifyou get a degree 4 equation, try something different.) c. The ellipse $72 + % and the line a: = 1. :l. The circle (a: 4)2 + (y 5)2 and the circle (a: + 3)2 + (y + 2)2 = 4. (Hint: this question doesn't need a long and complicated calculation. Look for an easier way to answer it.) e. The hyperbola 3% y; = 1 and the ellipse $32 + y; = 1. (Hint: ifyou get a degree 4 equation or an equation with difcult square roots, try a different approach or substitution). 2. At how many points can a line intersect a quadratic? Draw examples to show the different number of intersection points. (No equations are needed, just a simple drawing of the shapes.) Do the same for a line and a cubic, and then a line and a quartic. Make a proposition about the number of possible intersection points of a line and a degree n polynomial. (You don't have to argue for this proposition; just make a hypothesis based on the rst three cases.) (6)