91Ó°ÊÓ

Find the standard form of the equation of the ellipse with the given characteristics. Center: (0,4)\(; a=2 c ;\) vertices: (-4,4),(4,4)

Sketch the graph of the polar equation using symmetry, zeros, maximum \(r\) -values, and any other additional points. \(r=\frac{\pi}{3}\)

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. Use a graphing utility to graph the hyperbola and its asymptotes. \(4 x^{2}-9 y^{2}=36\)

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: \(y=1\)

(a) sketch the curve represented by the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. Adjust the domain of the resulting rectangular equation if necessary. \(x=t^{3}\) \(y=3 \ln t\)

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. (-2,20),(10,0)

Identify the conic and sketch its graph. \(r=\frac{3}{2-6 \cos \theta}\)

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. Use a graphing utility to graph the hyperbola and its asymptotes. \(25 x^{2}-4 y^{2}=100\)

Identify the conic and sketch its graph. \(r=\frac{3}{2+6 \sin \theta}\)

A point in polar coordinates is given. Convert the point to rectangular coordinates. \((-3,5 \pi / 6)\)