1. Transform the following equation of a circle into standard form, and find the center and radius:
2x^2 + 20x + 2y^2 - 8y = 14
2. Transform the following equation of an ellipse into standard form, and find the center, x-radius, y-radius, and focal radius. Sketch the graph, showing the coordinates of center and foci.
4x^2 + 16x + y^2 = 33
3. Transform the following equation of a hyperbola into standard form, and find the center, x-radius, y-radius, and focal radius. Sketch the graph, showing the coordinates of center and foci, as well as the asymptotes.
x^2 + 2x - 3y^2 + 18y = 2
4. The equation of a certain parabola is given to you in the form 2x^2 + 4x + 2y + 8 = 15.
(a) Transform the parabola's equation into the "vertex form" that we learned last fall.
(b) Give the coordinates of the vertex.
(c) Does the parabola open upward, downward, left, or right? How can you tell by looking only at the answer to part (a)?
(d) Sketch the graph, showing coordinates of all x- and y-intercepts.