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Magazine Problem 31
Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(1.5,-2.82)$$
Problem 31
Find the standard form of the equation of the hyperbola, (b) find the center, vertices, foci, and asymptotes of the hyperbola, and (c) sketch the hyperbola. Use a graphing utility to verify your graph. \(4 x^{2}-9 y^{2}=36\)
Problem 31
Identify and sketch the graph of the polar equation. Identify any symmetry and zeros of \(r .\) Use a graphing utility to verify your results. $$r=5 \cos 3 \theta$$
Problem 31
Sketch the circle. Identify its center and radius. $$x^{2}-14 x+y^{2}+8 y+40=0$$
Problem 32
Sketch the circle. Identify its center and radius. $$x^{2}+6 x+y^{2}-12 y+41=0$$
Problem 32
Use a graphing utility to graph the curve represented by the parametric equations. Use the graph and the Vertical Line Test to determine whether \(y\) is a function of \(x.\) $$\begin{aligned} &x=\sec \theta\\\ &y=\tan \theta \end{aligned}$$
Problem 32
Find the center, vertices, foci, and eccentricity of the ellipse, and sketch its graph. Use a graphing utility to verify your graph. $$\frac{(x+3)^{2}}{12}+\frac{(y-2)^{2}}{16}=1$$
Problem 32
Find the standard form of the equation of the hyperbola, (b) find the center, vertices, foci, and asymptotes of the hyperbola, and (c) sketch the hyperbola. Use a graphing utility to verify your graph. \(25 x^{2}-4 y^{2}=100\)
Problem 32
Identify and sketch the graph of the polar equation. Identify any symmetry and zeros of \(r .\) Use a graphing utility to verify your results. $$r=\sin 5 \theta$$
Problem 32
Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(-5.3,-0.78)$$
