91Ó°ÊÓ

In Exercises 19–30, use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation. $$ x=e^{-t}, \quad y=e^{3 t} $$

Finding an Equation of an Ellipse In Exercises \(29-34,\) find an equation of the ellipse. Center: \((0,0)\) Focus: \((5,0)\) Vertex: \((6,0)\)

Horizontal and Vertical Tangency In Exercises \(29-38\) , find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=4-t, \quad y=t^{2} $$

Finding Points of Intersection In Exercises \(25-32,\) find the points of intersection of the graphs of the equations. $$ \begin{array}{l}{r=3+\sin \theta} \\ {r=2 \csc \theta}\end{array} $$

Horizontal and Vertical Tangency In Exercises \(29-38\) , find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=t+1, \quad y=t^{2}+3 t $$

In Exercises 19–30, use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation. $$ x=e^{2 t}, \quad y=e^{t} $$

Rectangular-to-Polar Conversion In Exercises \(23-32\) convert the rectangular equation to polar form and sketch its graph. $$ x y=4 $$

Rectangular-to-Polar Conversion In Exercises \(23-32\) convert the rectangular equation to polar form and sketch its graph. $$ y^{2}=9 x $$

Finding Points of Intersection In Exercises \(25-32,\) find the points of intersection of the graphs of the equations. $$ \begin{array}{l}{r=\frac{\theta}{2}} \\ {r=2}\end{array} $$

Finding an Equation of an Ellipse In Exercises \(29-34,\) find an equation of the ellipse. Vertices: \((3,1),(3,9)\) Minor axis length: 6