Problem Set 2 - Math 133, Practice Problems: Conics,...

Math 133, Practice Problems: Conics, Parametric Equations and Polar Coordinates
The following questions are collected from some practice problems suggested to Math 122
students when they study conics, polar coordinates and parametric equations.
1. Write the equation of the conic x 2 + 6 x - 8 y - 23 = 0 in standard form, and then find
its vertex, focus and the equation of its directrix. (Think about similar questions for ellipses
and hyperbolas where you would find center, vertices, foci, and additionally asymptotes for
hyperbolas)
2. (a) Find the equation of the hyperbola with foci (2 , - 6) and (2 , 4) whose vertices are (2 , - 4)
and (2 , 2); and find the equation of its asymptotes.
(b) Find the equation of ellipse with vertices ( - 6 , 2) and (4 , 2) and foci ( - 4 , 2) and (2 , 2).
(c) Sketch the conics you found in (a) and (b). (Think about analogous questions for parabolas
where one is given, e.g. the focus and vertex).
3. (a) Describe the graph whose polar equation is r sin θ = 3. Be specific!
(b) Describe the graph whose polar equation is r = 4. Be specific!