91Ó°ÊÓ

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Foci: (0,±8)\(;\) asymptotes: \(y=\pm 4 x\)

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. . (2.5,1.58)

Use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{14}{14+17 \sin \theta}\)

Find the inclination \(\theta\) (in radians and degrees) of the line. \(6 x-2 y+8=0\)

Sketch the graph of the polar equation using symmetry, zeros, maximum \(r\) -values, and any other additional points. \(r=3+6 \sin \theta\)

Find the vertex, focus, and directrix of the parabola, and sketch its graph. \(y=\frac{1}{2} x^{2}\)

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. \(\frac{x^{2}}{5}+\frac{y^{2}}{9}=1\)

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. \(\frac{x^{2}}{64}+\frac{y^{2}}{28}=1\)

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Foci: (±10,0)\(;\) asymptotes: \(y=\pm \frac{3}{4} x\)

Find the inclination \(\theta\) (in radians and degrees) of the line. \(4 x+5 y-9=0\)