MATH 308 Midterm: MATH 308 2010 Winter Test 1
Document Summary
Be sure this exam has 12 pages including the cover. Rules governing formal examinations: each candidate must be prepared to produce, upon request, a. Find the two pairs of focuses and directrices of the ellipse x2 + 4y2 + 2x = 0. Let a > 0, b > 0, and f and g be the parabolas y2 = 4a(x + a) and y2 = 4b( x + b). The origin is the focus of both parabolas. Suppose f meets g at p above the x-axis. Use the re ection property of parabolas to prove that f and g cross at p at right angle. Page 4 of 12: classify the conics in r2 with the following equations. You do not need to nd their axes. (5 points) (a) 3x2 8xy + 2y2 2x + 4y 16 = 0 (5 points) (b) x2 + 8xy + 16y2 x + 8y 12 = 0.
