Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections

Determine the standard equation of the parabola whose focus is the point and directrix is the line .

The slope of the curve at is which of the following?

The length of the parametric curve is which of the following? A) B) C) D) E) The length integral cannot be computed analytically by the methods covered so far.

Find parametric equations for the curve .

Find parametric equations for the curve .

Find the arc length of the curve given by the parametric equations

Write the standard equation for the ellipse with the following characteristics: center , vertex , and focus .

Find the arc length of the parametric curve .

The area outside but inside is which of the following?

Give the polar coordinates of the point of intersection of the lines and .

Write the equation of in polar coordinates.

The equation of in Cartesian coordinates is which of the following?

Express the parametric curve by an equation in and

The slope of the curve at is which of the following?

A particle travels along the path (where length is in feet and time is in minutes). Find the speed of the particle and compute its displacement and the distance covered during the first minute of its motion.

Find the area of the shaded region in the following figure.

Write the equation in rectangular coordinates.

The surface area of the surface generated by revolving the parametric curve about the x-axis for is given by the formula . Compute the area of the surface generated by revolving the parametric curve about the x-axis.

Suppose that has polar coordinates , where x and y are not both zero. Find the polar coordinates of the following. A) B) C) D)

Find the area of the inner loop of .