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Magazine Problem 18
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=\tan ^{2} \theta, \quad y=\sec ^{2} \theta\)
Problem 19
(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). $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Parameter }} \\\ x=t^{2}-t+2, y=t^{3}-3 t &\quad t=-1 \end{array} $$
Problem 19
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=3 \cos \theta, \quad y=3 \sin \theta\)
Problem 19
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. $$ r=\frac{5}{-1+2 \cos \theta} $$
Problem 19
Find the points of intersection of the graphs of the equations.\(r=1+\cos \theta\) \(r=1-\sin \theta\)
Problem 19
Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ \left(\frac{5}{2}, \frac{4}{3}\right) $$
Problem 20
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. $$ r=\frac{-6}{3+7 \sin \theta} $$
Problem 20
Find the points of intersection of the graphs of the equations.\(r=2-3 \cos \theta\) \(r=\cos \theta\)
Problem 20
Find the vertex, focus, and directrix of the parabola. Then use a graphing utility to graph the parabola. $$ x^{2}-2 x+8 y+9=0 $$
Problem 20
Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (0,-5) $$
