Problem 2
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 \(3-5) .\) x^{2}+y^{2}+6 x-2 y+6=0
Problem 2
Name the conic (horizontal ellipse, vertical hyperbola, and so on) corresponding to the given equation. $$ \frac{x^{2}}{9}-\frac{y^{2}}{4}=1 $$
Problem 3
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 \(3-5) .\) 9 x^{2}+4 y^{2}+72 x-16 y+124=0
Problem 3
Plot the points whose polar coordinates are \((3,2 \pi)\), \(\left(-2, \frac{1}{3} \pi\right),\left(-2,-\frac{1}{4} \pi\right),(-1,1),(1,-4 \pi),\left(\sqrt{3},-\frac{7}{6} \pi\right),\left(-2, \frac{1}{4} \pi\right)\), and \(\left(-1,-\frac{1}{2} \pi\right) .\)
Problem 3
Sketch the graph of the given equation and find the area of the region bounded by it. $$ r=2+\cos \theta $$
Problem 3
Name the conic (horizontal ellipse, vertical hyperbola, and so on) corresponding to the given equation. $$ \frac{-x^{2}}{9}+\frac{y^{2}}{4}=1 $$
Problem 3
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. $$ x^{2}=-12 y $$
Problem 3
a parametric representation of a curve is given. $$ x=3 t-1, y=t ; 0 \leq t \leq 4 $$
Problem 4
a parametric representation of a curve is given. $$ x=4 t-2, y=2 t ; 0 \leq t \leq 3 $$
Problem 4
Plot the points whose polar coordinates are \(\left(3, \frac{9}{4} \pi\right)\), \(\left(-2, \frac{1}{2} \pi\right), \quad\left(-2,-\frac{1}{3} \pi\right), \quad(-1,-1), \quad(1,-7 \pi), \quad\left(-3,-\frac{1}{6} \pi\right)\), \(\left(-2,-\frac{1}{2} \pi\right)\), and \(\left(3,-\frac{33}{2} \pi\right) .\)
