91Ó°ÊÓ

In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Cycloid: \(\quad x=4(\theta - \sin\ \theta), \quad y=4(1 - \cos\ \theta)\)

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. \(r=\dfrac{9}{4}\)

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(\sqrt{3}, -1\right)\)

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. \(9x^2+9y^2+18x-18y+14=0\)

In Exercises 43-50, (a) use the discriminant to classify the graph, (b) use the Quadratic Formula to solve for \(y\), and (c) use a graphing utility to graph the equation. \(x^2+4xy+4y^2-5x-y-3=0\)

In Exercises 43-50, (a) use the discriminant to classify the graph, (b) use the Quadratic Formula to solve for \(y\), and (c) use a graphing utility to graph the equation. \(x^2+xy+4y^2+x+y-4=0\)

In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Ellipse \(\textit{Vertex or Vertices}\) \((2, \pi/2), (4, 3\pi/2)\)

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. \(16x^2+25y^2-32x-50y+16=0\)

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. \(r=-\dfrac{5}{2}\)

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(-1, \sqrt{3}\right)\)