91Ó°ÊÓ

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. \(\dfrac{x^2}{25}+\dfrac{y^2}{25}=1\)

In Exercises 29-34, use a graphing utility to graph the polar equation. Identify the graph. \(r=\dfrac{3}{-4+2 \cos\ \theta}\)

In Exercises 29-34, find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: \((\pm1, 0); \quad\) asymptotes: \(y=\pm5x\)

In Exercises 29-34, find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: \((0, \pm3); \quad\) asymptotes: \(y=\pm3x\)

In Exercises 27-36, use a graphing utility to graph the conic. Determine the angle \(\theta\) through which the axes are rotated.Explain how you used the graphing utility to obtain the graph. \(24x^2+18xy+12y^2=34\)

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

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. \(\left(8.25, 3.5\right)\)

In Exercises 29-32, eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola: \(\quad x=h+a\ \sec\ \theta, \quad y=k + b\ \tan\ \theta\)

In Exercises 29-34, use a graphing utility to graph the polar equation. Identify the graph. \(r=\dfrac{4}{1-2\ \cos\ \theta}\)

In Exercises 23-48, sketch the graph of the polar equation using symmetry, zeros, maximum \(r\)-values, and any other additional points. \(r=2(1\ +\ \cos\ \theta)\)