91Ó°ÊÓ

Sketch the graph of the given equation and find the area of the region bounded by it. $$ r^{2}=6 \cos 2 \theta $$

Find the coordinates of the focus and the equation of the directrix for each parabola. Make a sketch showing the parabola, its focus, and its directrix. $$ 3 x^{2}-9 y=0 $$

a parametric representation of a curve is given. $$ x=s, y=\frac{1}{s} ; 1 \leq s \leq 10 $$

Name the conic or limiting form represented by the given equation. Usually you will need to use the process of completing the square (see Examples \(3-5) .\) 4 x^{2}+4 y^{2}+8 x-28 y-11=0

Name the conic (horizontal ellipse, vertical hyperbola, and so on) corresponding to the given equation. $$ x^{2}-4 y^{2}=4 $$

a parametric representation of a curve is given. $$ x=t^{3}-4 t, y=t^{2}-4 ;-3 \leq t \leq 3 $$

Find polar coordinates of the points whose Cartesian coordinates are given. (a) \((3 \sqrt{3}, 3)\) (b) \((-2 \sqrt{3}, 2)\) (c) \((-\sqrt{2},-\sqrt{2})\) (d) \((0,0)\)

Sketch the graph of the given equation, indicating vertices, foci, and asymptotes (if it is a hyperbola). $$ \frac{x^{2}}{16}+\frac{y^{2}}{4}=1 $$

Find the standard equation of each parabola from the given information. Assume that the vertex is at the origin. Focus is at \((2,0)\)

Name the conic or limiting form represented by the given equation. Usually you will need to use the process of completing the square (see Examples \(3-5) .\) 3 x^{2}+3 y^{2}-6 x+12 y+60=0