91影视

The pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{aligned} &x=3 \cos t \\ &y=4 \sin t \end{aligned} $$

Convert the rectangular equation to polar form and sketch its graph. $$ x^{2}+y^{2}=16 $$

For the following exercises, consider the following polar equations of conics. Determine the eccentricity and identify the conic. $$ r=\frac{5}{2+\sin \theta} $$

Use the integration capabilities of a calculator to approximate the length of the curve.[T] \(r=2 \theta^{2}\) on the interval \(0 \leq \theta \leq \pi\)

For the following exercises, consider the following polar equations of conics. Determine the eccentricity and identify the conic. $$ r=\frac{5}{-1+2 \sin \theta} $$

Use the integration capabilities of a calculator to approximate the length of the curve.[T] \(r=\sin (3 \cos \theta)\) on the interval \(0 \leq \theta \leq \pi\)

For the following exercises, find \(d y / d x\) at the value of the parameter.\(x=\sqrt{t}, \quad y=2 t+4, \quad t=9\)

The pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{aligned} &x=2 \cos (3 t) \\ &y=5 \sin (3 t) \end{aligned} $$

Convert the rectangular equation to polar form and sketch its graph. $$ x^{2}-y^{2}=16 $$

The pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{aligned} &x=3 \cosh (4 t) \\ &y=4 \sinh (4 t) \end{aligned} $$