91Ó°ÊÓ

(a) Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C .\) /b ) Sketch the graph of \(C\) and indicate the orientation. $$ x=4 t^{2}-5, \quad y=2 t+3 ; \quad t \text { in } \mathbb{R} $$

Sketch the graphs of \(C_{1}, C_{2}, C_{3},\) and \(C_{4},\) and indicate their orientations. $$ \begin{array}{llll} C_{1}: & x=1, & y=\sqrt{16-t^{2}}: & -4 \leq t \leq 4 \\ C_{2}: & x=-\sqrt{16-t}, & y=-\sqrt{t:} & 0 \leq t \leq 16 \\ C_{3}: & x=4 \cos t, & y=4 \sin t: & 0 \leq t \leq 2 \pi \\ C_{4}: & x=e^{t}, & y=-\sqrt{16-e^{2 t}} ; & t \leq \ln 4 \end{array} $$

Find the area of the region bounded by the graph of the polar equation. $$ r=\sin 2 \theta $$

Exer. \(1-8\) : Find the slopes of the tangent line and the normal line at the point on the curve that corresponds to \(t=1\). $$ x=e^{t}, \quad y=e^{-2 t} ; \quad t \text { in } R $$

(a) Find the eccentricity and classify the conic. (b) Sketch the graph and label the vertices. \(r=\frac{3}{2+2 \cos \theta}\)

Sketch the graph of the polar equation. $$ r=3 \cos \theta $$

(a) Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C .\) /b ) Sketch the graph of \(C\) and indicate the orientation. $$ x=t^{3}, \quad y=t^{2} ; \quad t \text { in } \mathbb{R} $$

Sketch the graph of the polar equation. $$ r=-2 \sin \theta $$

Exer. \(1-8\) : Find the slopes of the tangent line and the normal line at the point on the curve that corresponds to \(t=1\). $$ x=\sqrt{t}, \quad y=3 t+4: \quad t \geq 0 $$

(a) Find the eccentricity and classify the conic. (b) Sketch the graph and label the vertices. \(r=\frac{3}{2-2 \sin \theta}\)