91Ó°ÊÓ

Convert the rectangular coordinates to polar coordinates. $$(3,3 \sqrt{3})$$

Identify the conic whose equation is given and find its graph. If it is an ellipse, list its center, vertices, and foci. If it is a hyperbola, list its center, vertices, foci, and asymptotes. $$\frac{(y+3)^{2}}{25}-\frac{(x+1)^{2}}{16}=1$$

Sketch the graph of the equation and label the vertices. $$r=\frac{10}{4-3 \sin \theta}$$

The given curve is part of the graph of an equation in \(x\) and \(y .\) Find the equation by eliminating the parameter. $$x=\sqrt{t}, \quad y=t^{4}-1, \quad t \geq 0$$

In Exercises \(17-28,\) determine the vertex, focus, and directrix of the parabola without graphing and state whether it opens upward, downward, left, or right. $$y=3 x^{2}+x-4$$

Find the equation of the ellipse that satisfies the given conditions. Center (0,0)\(;\) endpoints of major and minor axes: (0,-7), (0,7),(-3,0),(3,0).

Sketch the graph of the equation and label the vertices. $$r=\frac{12}{3+4 \sin \theta}$$

Find the equation of the ellipse that satisfies the given conditions. Center (0,0)\(;\) vertices (8,0) and (-8,0)\(;\) minor axis of length 8.

Convert the rectangular coordinates to polar coordinates. $$(-\sqrt{2}, \sqrt{6})$$

In Exercises \(17-28,\) determine the vertex, focus, and directrix of the parabola without graphing and state whether it opens upward, downward, left, or right. $$y=-3 x^{2}+4 x-1$$