91Ó°ÊÓ

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola, and sketch its graph using the asymptotes as an aid. \(\frac{(y+6)^{2}}{1 / 9}-\frac{(x-2)^{2}}{1 / 4}=1\)

Find the inclination \(\theta\) (in radians and degrees) of the line with a slope of \(m\). \(m=\frac{3}{4}\)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0,±5) ; passes through the point (4,2)

Plot the point given in polar coordinates and find two additional polar representations of the point, using \(-2 \pi<\theta<2 \pi\). (-3,-1.57)

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola, and sketch its graph using the asymptotes as an aid. \(\frac{(y-1)^{2}}{1 / 4}-\frac{(x+3)^{2}}{1 / 16}=1\)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis; passes through the points (0,6) and (3,0)

Plot the point given in polar coordinates and find two additional polar representations of the point, using \(-2 \pi<\theta<2 \pi\). (-5,-2.36)

Find the inclination \(\theta\) (in radians and degrees) of the line with a slope of \(m\). \(m=-\frac{5}{2}\)

Test for symmetry with respect to \(\boldsymbol{\theta}=\pi / 2,\) the polar axis, and the pole. \(r^{2}=25 \sin 2 \theta\)

Identify the conic and sketch its graph. \(r=\frac{6}{1+\cos \theta}\)