91Ó°ÊÓ

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=1-t, \quad y=t^{2} $$

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. \(x=4 \sec \theta, \quad y=3 \tan \theta\)

Find an equation of the parabola. Axis is parallel to \(y\) -axis; graph passes through \((0,3),(3,4)\), and \((4,11)\).

Convert the rectangular equation to polar form and sketch its graph. $$ x^{2}+y^{2}-2 a x=0 $$

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. \(x=\cos ^{3} \theta, \quad y=\sin ^{3} \theta\)

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=t+1, \quad y=t^{2}+3 t $$

Find an equation of the parabola. Directrix: \(y=-2\); endpoints of latus rectum are \((0,2)\) and \((8,2) .\)

Use a graphing utility to approximate the points of intersection of the graphs of the polar equations. Confirm your results analytically.\(r=3(1-\cos \theta)\) \(r=\frac{6}{1-\cos \theta}\)

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. \(x=t^{3}, \quad y=3 \ln t\)

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=1-t, \quad y=t^{3}-3 t $$