91Ó°ÊÓ

Arc Length In Exercises 49-54, find the arc length of the curve on the given interval. $$\begin{array}{ll}{\text { Parametric Equations }} & {\text { Interval }} \\\ {x=\arcsin t, \quad y=\ln \sqrt{1-t^{2}} } & {0 \leq t \leq \frac{1}{2}}\end{array}$$

Area Sketch the strophoid \(r=\sec \theta-2 \cos \theta, \quad-\frac{\pi}{2}<\theta<\frac{\pi}{2}\) Convert this equation to rectangular coordinates. Find the area enclosed by the loop.

Finding the Arc Length of a Polar Curve In Exercises \(53-58\) , find the length of the curve over the given interval. \(r=8, \quad\left[0, \frac{\pi}{6}\right]\)

Arc Length In Exercises 49-54, find the arc length of the curve on the given interval. $$\begin{array}{ll}{\text { Parametric Equations }} & {\text { Interval }} \\\ {x=\sqrt{t}, \quad y=3 t-1 } & {0 \leq t \leq 1}\end{array}$$

Classifying the Graph of an Equation In Exercises \(51-56\) , classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$3(x-1)^{2}=6+2(y+1)^{2}$$

Graphing a Polar Equation In Exercises \(45-54\) , use a graphing utility to graph the polar equation. Find an interval for \(\theta\) over which the graph is traced only once. $$r^{2}=4 \sin 2 \theta$$

Arc Length In Exercises 49-54, find the arc length of the curve on the given interval. $$\begin{array}{ll}{\text { Parametric Equations }} & {\text { Interval }} \\\ {x=t, \quad y=\frac{t^{5}}{10}+\frac{1}{6 t^{3}}} & {1 \leq t \leq 2}\end{array}$$

Classifying the Graph of an Equation In Exercises \(51-56\) , classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$9(x+3)^{2}=36-4(y-2)^{2}$$

Classifying the Graph of an Equation In Exercises \(51-56\) , classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$9 x^{2}+9 y^{2}-36 x+6 y+34=0$$

Verifying a Polar Equation Convert the equation \(r=2(h \cos \theta+k \sin \theta)\) to rectangular form and verify that it is the equation of a circle. Find the radius and the rectangular coordinates of the center of the circle.