91Ó°ÊÓ

(a) Find the eccentricity and classify the conic. (b) Sketch the graph and label the vertices. \(r=\frac{4}{\cos \theta-2}\)

Exer. \(1-8\) : Find the slopes of the tangent line and the normal line at the point on the curve that corresponds to \(t=1\). $$ x=2 \sin t, \quad y=3 \cos t ; \quad 0 \leq t \leq 2 \pi $$

(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. $$ x=e^{t}, \quad y=e^{-2 t} ; \quad t \text { in } \mathbb{R} $$

Let \(C\) be the given parametrized curve. (a) Express \(d y / d x\) in terms of \(t\). (b) Find the values of \(t\) that correspond to horizontal or vertical tangent lines to the graph of \(C\). (c) Express \(d^{2} y / d x^{2}\) in terms of \(t\). $$ x=t^{2}, \quad y=2 t^{3}+4 t-1 ; \quad t \text { in } \mathbb{R} $$

Sketch the graph of the polar equation. $$ r=4-4 \sin \theta $$

Exer. \(1-8\) : Find the slopes of the tangent line and the normal line at the point on the curve that corresponds to \(t=1\). $$ x=\cos t-2, \quad y=\sin t+3 ; \quad 0 \leq t \leq 2 \pi $$

Sketch the graph of the polar equation. $$ r=-6(1+\cos \theta) $$

(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. $$ x=\sqrt{t}, \quad y=3 t+4 ; \quad t \geq 0 $$

(a) Find the eccentricity and classify the conic. (b) Sketch the graph and label the vertices. \(r=\frac{4 \sec \theta}{2 \sec \theta-1}\)

Let \(C\) be the given parametrized curve. (a) Express \(d y / d x\) in terms of \(t\). (b) Find the values of \(t\) that correspond to horizontal or vertical tangent lines to the graph of \(C\). (c) Express \(d^{2} y / d x^{2}\) in terms of \(t\). $$ x=t-2 \sin t, \quad y=1-2 \cos t: \quad t \text { in } \mathbb{R} $$