conics, and model the paths traveled by planets, satellites, and other bodies whose motions are driven by inverse square forces. we will see that once the path of a moving
body is known to be a conic, we immediately have information about the body’s velocity and the force that drives it. Planetary motion is best described with the help of polar coordinates, so we also investigate curves, derivatives, and integrals in this new coordinate system
An ellipse is the set of points in a plane whose distances from two fixed points
in the plane have a constant sum. The two fixed points are the foci of the
ellipse The line through the foci of an ellipse is the ellipse’s focal axis. The point on the
axis halfway between the foci is the center. The points where the focal axis andAAtheir use as reflectors of light and radio
waves. Rays originating at a parabola’s focus are reflected out of the parabola parallel to
the parabola’s axis Moreover, the time any ray takes from
the focus to a line parallel to the parabola’s directrix (thus perpendicular to its axis) is the
same for each of the rays. These properties are used by flashlight, headlight, and spotlight
reflectors and by microwave broadcast antennas. A hyperbola is the set of points in a plane whose distances from two fixed points
in the plane have a constant difference. The two fixed points are the foci of the
hyperbolaA The chief applications of parabolas involve their use as reflectors of light and radio
waves. Rays originating at a parabola’s focus are reflected out of the parabola parallel to
the parabola’s axis Moreover, the time any ray takes from
the focus to a line parallel to the parabola’s directrix (thus perpendicular to its axis) is the
same for each of the rays. These properties are used by flashlight, headlight, and spotlight reflectors and by microwave broadcast antennas