91Ó°ÊÓ

What is the polar equation of a circle of radius \(|a|\) centered at the origin?

What is the polar equation of the vertical line \(x=5 ?\)

Explain the Cartesian-to-polar method for graphing polar curves.

Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates. \(r=2 \sin 3 \theta ;\) at the tips of the leaves

Consider the following parametric equations. a. Make a brief table of values of \(t, x,\) and \(y.\) b. Plot the \((x, y)\) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing \(t\)). c. Eliminate the parameter to obtain an equation in \(x\) and \(y.\) d. Describe the curve. $$x=-t+6, y=3 t-3 ;-5 \leq t \leq 5$$

Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates. $$r=2 \theta ;\left(\frac{\pi}{2}, \frac{\pi}{4}\right)$$

Find an equation of the following parabolas, assuming the vertex is at the origin. A parabola symmetric about the \(y\) -axis that passes through the point (2,-6)

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at the origin with radius \(12,\) generated clockwise with initial point \((0,12)\)

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at \((2,3)\) with radius \(1,\) generated counterclockwise

Find parametric equations for the following circles and give an interval for the parameter values. Graph the circle and find a description in terms of \(x\) and \(y .\) Answers are not unique. A circle centered at \((2,0)\) with radius \(3,\) generated clockwise