91Ó°ÊÓ

In Exercises 29-36, use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. \(\left(8.2, -3.2\right)\)

In Exercises 23-48, sketch the graph of the polar equation using symmetry, zeros, maximum \(r\)-values, and any other additional points. \(r=2 - 4\ \cos\ \theta)\)

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

In Exercises 35-46, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: \((4, 1), (4, 9); \quad\) foci: \((4, 0), (4, 10)\)

In Exercises 33-40, use the results of Exercises 29-32 to find a set of parametric equations for the line or conic. Ellipse: vertices: \((\pm5, 0); \quad\) foci: \((\pm4, 0)\)

In Exercises 33-46, find the vertex, focus, and directrix of the parabola, and sketch its graph. \(x^2 + 6y = 0\)

In Exercises 23-48, sketch the graph of the polar equation using symmetry, zeros, maximum \(r\)-values, and any other additional points. \(r=3 - 4\ \cos\ \theta)\)

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. \(\dfrac{x^2}{4/9}+\dfrac{(y+1)^2}{4/9}=1\)

In Exercises 37-46, find the angle \(\theta\) (in radians and degrees)between the lines. \(3x + y = 3\) \(x - y = 2\)

In Exercises 37-46, find the angle \(\theta\) (in radians and degrees)between the lines. \(x + 3y = 2\) \(x - 2y = -3\)