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Magazine Problem 16
Sketch a graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$4 x=-y^{2}$$
Problem 17
Sketch a graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$8 y=-3 x^{2}$$
Problem 17
Express the following polar coordinates in Cartesian coordinates. \(\left(1,-\frac{\pi}{3}\right)\)
Problem 17
Find the points at which the following polar curves have a horizontal or a vertical tangent line. $$r=\sin 2 \theta$$
Problem 17
Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y.\) b. Describe the curve and indicate the positive orientation. $$x=\cos t, y=\sin ^{2} t ; 0 \leq t \leq \pi$$
Problem 18
Express the following polar coordinates in Cartesian coordinates. \(\left(2, \frac{7 \pi}{4}\right)\)
Problem 18
Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y.\) b. Describe the curve and indicate the positive orientation. $$x=1-\sin ^{2} s, y=\cos s ; \pi \leq s \leq 2 \pi$$
Problem 18
Sketch a graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$12 x=5 y^{2}$$
Problem 18
Find the points at which the following polar curves have a horizontal or a vertical tangent line. $$r=3+6 \sin \theta$$
Problem 19
Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y.\) b. Describe the curve and indicate the positive orientation. $$x=r-1, y=r^{3} ;-4 \leq r \leq 4$$
