Exam 10: Parametric Equations and Polar Coordinates

Find the length of the polar curve.

Find the point(s) on the curve where the tangent is horizontal.

Find a polar equation for the curve represented by the given Cartesian equation.Select the correct Answer

Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse.

Describe the motion of a particle with position as varies in the given interval

Find the point(s) on the curve where the tangent is horizontal.Select the correct Answer

Select the correct Answer: for each question. -Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus.Its perihelion distance (minimum distance from the planet to the sun) is approximately km, and its aphelion distance (maximum distance from the planet to the sun) is approximately km.Approximate the eccentricity of the planet's orbit.Round to three decimal places.

Find the area of the region that lies inside the first curve and outside the second curve.Select the correct Answer

Find an equation of the hyperbola with vertices and asymptotes

Eliminate the parameter to find a Cartesian equation of the curve.

Find the eccentricity of the conic.Select the correct Answer

Select the correct Answer: for each question. -Find an equation of the ellipse that satisfies the given conditions.Foci: (0, ± 8), vertices

Find the area of the region that lies inside the first curve and outside the second curve.

Select the correct Answer: for each question. -Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix

Select the correct Answer: for each question -Find the length of the polar curve.

Write a polar equation in r and θ of an ellipse with the focus at the origin, with the eccentricity and directrix

Find an equation of the ellipse that satisfies the given conditions.Foci: (0, ± 8), vertices