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Magazine 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
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
Name the conic corresponding to the given equation. \(\frac{-x^{2}}{9}+\frac{y}{4}=0\)
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. $$ 9 x^{2}+4 y^{2}+72 x-16 y+160=0 $$
Problem 5
\(r=3-3 \sin \theta\)
Problem 6
Name the conic corresponding to the given equation. \(\frac{-x^{2}}{9}=\frac{y}{4}\)
Problem 6
In Problems \(1-32\), sketch the graph of the given polar equation and verify its symmetry (see Examples 1-3). \(r=4 \sin \theta\)
Problem 6
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. $$y^{2}+3 x=0$$
Problem 6
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) \(\left(3 \sqrt{2}, \frac{7}{2} \pi\right)\) (b) \(\left(-1, \frac{15}{4} \pi\right)\) (c) \(\left(-\sqrt{2},-\frac{2}{3} \pi\right)\) (d) \(\left(-2 \sqrt{2}, \frac{29}{2} \pi\right)\)
Problem 6
Name the conic or limiting form represented by the given equation. Usually you will need to use the process of completing the square. $$ 16 x^{2}+9 y^{2}+192 x+90 y+1000=0 $$
