Exam 10: Parametric and Polar Curves; Conic Sections

Find the equation of the curve described. The ellipse with a major axis length of , a minor axis of , center at , and foci on .

Find the area bounded by .

Express the given curve in polar coordinates.

The area in one petal of is given by

Find the area bounded by .

State the name that describes the polar curve most precisely.

Find the arclength of the curve . Give a numeric answer to three decimal places.

Sketch the curve in polar coordinates.

Find the vertex of the parabola in the x'y'-coordinate system.

Identify the type of conic section by transforming to rectangular coordinates.

What are the polar coordinates of a point whose rectangular coordinates are given as ?Note: n is an integer.

Put the rectangular equation y = 3x² + 1 into parametric form.

Find the asymptotes of .

Find the arclength of the curve

Rotate the coordinates to remove the xy-term. Then, name the conic.

Convert the following equation to polar coordinates.

Find the polar equation for the conic that has its focus at the pole and its directrix is units below the pole and its eccentricity is .

Find the approximate arc length of x = 3t² , y = 4t³ + 2 , over the interval .

Find the equation of the hyperbola with foci and vertices units apart.

Find the slope of the tangent to the curve at the point corresponding to .