Calculus Early Transcendentals

The graph of the following curve is given. Find the area that it encloses.

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

Consider the polar equation .(a) Find the eccentricity and an equation of the directrix of the conic.(b) Identify the conic.(c) Sketch the curve.

Find the area that the curve encloses.

The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and one focus at the Sun. The length of its major axis is AU. [An astronomical unit (AU) is the mean distance between Earth and the Sun, about 93 million miles.] Find the maximum distance from the comet to the Sun. (The perihelion distance from a planet to the Sun is and the aphelion distance is .) Find the answer in AU and round to the nearest hundredth.

Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.

The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun.

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

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

Consider the polar equation .(a) Find the eccentricity and an equation of the directrix of the conic.(b) Identify the conic.(c) Sketch the curve.

Find the area enclosed by the curve .

Find the length of the polar curve.

Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .

Find the area of the region enclosed by one loop of the curve.

Find the Cartesian coordinates of the point .

Find the eccentricity of the conic.

Write a polar equation in r and  of an ellipse with the focus at the origin, with the eccentricity and vertex at .

Sketch the polar curve with the given equation.

Find the polar equation for the curve represented by the given Cartesian equation.

Find a Cartesian equation for the curve described by the given polar equation.