Problem 4
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 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 \(\left(3,-\frac{33}{2} \pi\right) .\)
Problem 4
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. $$ x^{2}=-16 y $$
Problem 4
a parametric representation of a curve is given. $$ x=4 t-2, y=2 t ; 0 \leq t \leq 3 $$
Problem 5
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. $$ y^{2}=x $$
Problem 5
Sketch the graph of the given equation and find the area of the region bounded by it. $$ r=3-3 \sin \theta $$
Problem 5
Plot the points whose polar coordinates follow. For each point, give four other pairs of polar coordinates, two with positive \(r\) and two with negative \(r\). (a) \(\left(1, \frac{1}{2} \pi\right)\) (b) \(\left(-1, \frac{1}{4} \pi\right)\) (c) \(\left(\sqrt{2},-\frac{1}{3} \pi\right)\) (d) \(\left(-\sqrt{2}, \frac{5}{2} \pi\right)\)
Problem 5
a parametric representation of a curve is given. $$ x=4-t, y=\sqrt{t} ; 0 \leq t \leq 4 $$
Problem 5
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+160=0
Problem 5
Name the conic (horizontal ellipse, vertical hyperbola, and so on) corresponding to the given equation. $$ \frac{-x^{2}}{9}+\frac{y}{4}=0 $$
