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Magazine Problem 83
Find the standard form of the equation of the parabola with the given characteristics. $$\text { Vertex: }(-2,0) ; \text { focus: }\left(-\frac{3}{2}, 0\right)$$
Problem 83
Find the exact value of the trigonometric expression when \(u\) and \(v\) are in Quadrant IV and \(\sin u=-\frac{3}{5}\) and \(\cos v=1 / \sqrt{2}\). $$\cos (u-v)$$
Problem 84
Describe the graph of the polar equation and find the corresponding rectangular equation. Sketch its graph. $$\theta=\frac{7 \pi}{6}$$
Problem 84
Find the standard form of the equation of the parabola with the given characteristics. $$\text { Vertex: }(3,-3) ; \text { focus: }\left(3,-\frac{9}{4}\right)$$
Problem 85
Describe the graph of the polar equation and find the corresponding rectangular equation. Sketch its graph. $$r=3 \sec \theta$$
Problem 85
Find the standard form of the equation of the parabola with the given characteristics. Vertex: (5,2)\(;\) focus: (3,2)
Problem 86
Find the standard form of the equation of the parabola with the given characteristics. Vertex: (-1,2)\(;\) focus: (-1,0)
Problem 86
Describe the graph of the polar equation and find the corresponding rectangular equation. Sketch its graph. $$r=2 \csc \theta$$
Problem 87
The center of a Ferris wheel lies at the pole of the polar coordinate system, where the distances are in feet. Passengers enter a car at \((30,-\pi / 2) .\) It takes 45 seconds for the wheel to complete one clockwise revolution. (a) Write a polar equation that models the possible positions of a passenger car. (b) Passengers enter a car. Find and interpret their coordinates after 15 seconds of rotation. (c) Convert the point in part (b) to rectangular coordinates. Interpret the coordinates.
Problem 87
Find the standard form of the equation of the parabola with the given characteristics. Vertex: (0,4)\(;\) directrix: \(y=2\)
