91Ó°ÊÓ

Express the following Cartesian coordinates in polar coordinates in at least two different ways. $$(1, \sqrt{3})$$

Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in \(x\) and \(y\). $$x=t, y=\sqrt{4-t^{2}}$$

Express the following Cartesian coordinates in polar coordinates in at least two different ways. $$(0,-9)$$

Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in \(x\) and \(y\). $$x=\sqrt{t+1}, y=\frac{1}{t+1}$$

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the right lobe of \(r=\sqrt{\cos 2 \theta}\)

Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin. A parabola with focus at (-4,0)

Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the circle \(r=8 \sin \theta\)

Eliminating the parameter Eliminate the parameter to express the following parametric equations as a single equation in \(x\) and \(y\). $$x=\tan t, y=\sec ^{2} t-1$$

Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin. A parabola symmetric about the \(y\) -axis that passes through the point (2,-6)

Express the following Cartesian coordinates in polar coordinates in at least two different ways. $$(-4,4 \sqrt{3})$$