Problem 1
a parametric representation of a curve is given.
$$
x=3 t, y=2 t ;-\infty
Problem 1
Plot the points whose polar coordinates are \(\left(3, \frac{1}{3} \pi\right)\), \(\left(1, \frac{1}{2} \pi\right),\left(4, \frac{1}{3} \pi\right),(0, \pi),(1,4 \pi),\left(3, \frac{11}{7} \pi\right),\left(\frac{5}{3}, \frac{1}{2} \pi\right)\), and \((4,0) .\)
Problem 1
Sketch the graph of the given equation and find the area of the region bounded by it. $$ r=a, a>0 $$
Problem 1
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. $$ y^{2}=4 x $$
Problem 1
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 1
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}-2 x+2 y+1=0
Problem 2
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. $$ y^{2}=-12 x $$
Problem 2
a parametric representation of a curve is given.
$$
x=2 t, y=3 t ;-\infty
Problem 2
Name the conic (horizontal ellipse, vertical hyperbola, and so on) corresponding to the given equation. $$ \frac{x^{2}}{9}-\frac{y^{2}}{4}=1 $$
Problem 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
