91影视

Convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=2 t-3, \quad y=6 t-7 $$

Find the area of the described region.Enclosed by \(r=1+\sin \theta\)

For the following exercises, find all points on the curve that have the given slope.\(x=t+\frac{1}{t}, \quad y=t-\frac{1}{t}\), slope \(=1\)

The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point in \((0,2 \pi]\). Round to three decimal places. $$ (8,15) $$

For the following exercises, determine the equation of the parabola using the information given. $$ \text { Focus }(-3,5) \text { and directrix } y=1 $$

Convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=t^{2}, \quad y=t^{3} $$

The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point in \((0,2 \pi]\). Round to three decimal places. $$ (-6,8) $$

For the following exercises, determine the equation of the parabola using the information given. $$ \text { Focus }\left(\frac{5}{2},-4\right) \text { and directrix } x=\frac{7}{2} $$

For the following exercises, find all points on the curve that have the given slope.\(x=2+\sqrt{t}, \quad y=2-4 t\), slope \(=0\)

The rectangular coordinates of a point are given. Find two sets of polar coordinates for the point in \((0,2 \pi]\). Round to three decimal places. $$ (4,3) $$