91Ó°ÊÓ

Rectangular-to-Polar Conversion In Exercises 15- 24 , the rectangular coordinates of a point are given. Plot the point and find two sets. of polar coordinates for the point for \(0 \leq \theta<2 \pi\). $$(0,-9)$$

Sketching a Parabola In Exercises \(11-16,\) find the vertex, focus, and directrix of the parabola, and sketch its graph. $$x^{2}-2 x-4 y-7=0$$

Using Parametric Equations In Exercises \(5-22,\) sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$x=|t-1|, \quad y=t+2$$

Identifying and Sketching a Conic In Exercises \(13-22\) , find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm your results. $$r=\frac{4}{1+\cos \theta}$$

Finding the Area of a Polar Region In Exercises \(7-18\) , find the area of the region. Interior of \(r=1-\cos \theta\)

Using Parametric Equations In Exercises \(5-22,\) sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$x=e^{t}, \quad y=e^{3 t}+1$$

Rectangular-to-Polar Conversion In Exercises 15- 24 , the rectangular coordinates of a point are given. Plot the point and find two sets. of polar coordinates for the point for \(0 \leq \theta<2 \pi\). $$(-3,4)$$

Finding the Standard Equation of a Parabola In Exercises \(17-24\) , find the standard form of the equation of the parabola with the given characteristics. Vertex: \((5,4)\) Focus: \((3,4)\)

Finding the Area of a Polar Region In Exercises \(7-18\) , find the area of the region. Interior of \(r^{2}=4 \cos 2 \theta\)

Identifying and Sketching a Conic In Exercises \(13-22\) , find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm your results. $$r=\frac{6}{-2+3 \cos \theta}$$