91Ó°ÊÓ

Find the vertex, focus, and directrix of the parabola. Then use a graphing utility to graph the parabola. $$ y^{2}+x+y=0 $$

(a) use a graphing utility to graph the curve represented by the parametric equations, (b) use a graphing utility to find \(d x / d t, d y / d t\), and \(d y / d x\) at the given value of the parameter, (c) find an equation of the tangent line to the curve at the given value of the parameter, and (d) use a graphing utility to graph the curve and the tangent line from part (c). $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Parameter }} \\\ x=2 t, y=t^{2}-1 &\quad t=2 \end{array} $$

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3,-2) $$

Find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. $$ r(2+\sin \theta)=4 $$

Find the points of intersection of the graphs of the equations.\(r=1+\cos \theta\) \(r=1-\cos \theta\)

(a) use a graphing utility to graph the curve represented by the parametric equations, (b) use a graphing utility to find \(d x / d t, d y / d t\), and \(d y / d x\) at the given value of the parameter, (c) find an equation of the tangent line to the curve at the given value of the parameter, and (d) use a graphing utility to graph the curve and the tangent line from part (c). $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Parameter }} \\\ x=t-1, y=\frac{1}{t}+1& \quad t=1 \end{array} $$

Find the points of intersection of the graphs of the equations.\(r=3(1+\sin \theta)\) \(r=3(1-\sin \theta)\)

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3 \sqrt{2}, 3 \sqrt{2}) $$

Find the vertex, focus, and directrix of the parabola. Then use a graphing utility to graph the parabola. $$ y=-\frac{1}{6}\left(x^{2}-8 x+6\right) $$

Find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. $$ r(3-2 \cos \theta)=6 $$