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Magazine Problem 50
In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Cycloid: \(\quad x=\theta + \sin\ \theta, \quad y= 1 - \cos\ \theta\)
Problem 51
In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. \(r=\dfrac{5\pi}{8}\)
Problem 51
In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(6, 9\right)\)
Problem 51
In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Prolate cycloid: \(\quad x= \theta - \frac{3}{2} \sin\ \theta, \quad y=1- \frac{3}{2} \cos\ \theta\)
Problem 51
In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Ellipse \(\textit{Vertex or Vertices}\) \((20, 0), (4, \pi)\)
Problem 51
In Exercises 51-58, find the distance between the point and the line. \(\textit{Point}\) \((0, 0)\) \(\textit{Line}\) \(4x + 3y = 0\)
Problem 51
In Exercises 29-52, identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(9x^2+25y^2-36x-50y+60=0\)
Problem 51
In Exercises 51-56, sketch (if possible) the graph of the degenerate conic. \(y^2-16x^2=0\)
Problem 52
In Exercises 29-52, identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(16x^2+16y^2-64x+32y+55=0\)
Problem 52
In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. \(r=-\dfrac{\pi}{10}\)
