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

The area inside and outside is approximately which of the following?

Find the polar equation of the line .

Find the polar equation of the line through orthogonal to the line .

Write the equation of in polar coordinates.

Find the area of the inner loop of .

Find the length of the polar curve . Use: .

Find the polar equation of the line .

Find the equation for the ellipse with foci at and and eccentricity .

Find the slope of the tangent line to the curve at .

The right hyperbola is parametrized by which of the following equations?

Match the polar equations with their Cartesian form A) B) C) D) i) ii) iii) iv)

Find the area enclosed by one turn of the logarithmic spiral .

Match the polar equations with their Cartesian form A) B) C) D) i) ii) iii) iv)

A moving particle is following the path . At the particle leaves the path on a straight line tangent to the path. If the particle maintains the same speed as when it left the path, what are the x- and y-coordinates of the particle's position when ?

Find the speed at and the arc length of the parametric curve between the points (corresponding to ) and (corresponding to ).

Find the area inside the cardioid and below the line

The area inside but outside is approximately which of the following?

Compute the length of the parametric curve .

Find the speed and the length of the curve.

Identify the type of conic section whose polar equation is .