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Magazine Problem 15
Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=\sec t, \quad y=\tan t $$
Problem 15
Plot the point whose polar coordinates are given by first constructing the angle \(\theta\) and then marking off the distance \(r\) along the ray. $$ \left(-4, \frac{3 \pi}{4}\right) $$
Problem 15
For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line.\(x=8+2 t, \quad y=1\)
Problem 16
Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=\ln (2 t), \quad y=t^{2} $$
Problem 16
Plot the point whose polar coordinates are given by first constructing the angle \(\theta\) and then marking off the distance \(r\) along the ray. $$ \left(1, \frac{\pi}{4}\right) $$
Problem 16
For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line.\(x=4-3 t, \quad y=-2+6 t\)
Problem 16
Identify and create a graph of the conic section described by the equation $$ r=\frac{4}{1-0.8 \sin \theta} $$
Problem 17
Identify the conic and calculate the angle of rotation of axes for the curve described by the equation $$ 13 x^{2}-6 \sqrt{3} x y+7 y^{2}-256=0 $$
Problem 17
Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=e^{t}, \quad y=e^{2 t} $$
Problem 17
For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line.\(x=-5 t+7, \quad y=3 t-1\)
