# Introduction to Conic Sections in Polar Coordinates

### Learning Objectives

By the end of this section, you will be able to:- Identify a conic in polar form.
- Graph the polar equations of conics.
- Deﬁne conics in terms of a focus and a directrix.

**Figure 1.**Planets orbiting the sun follow elliptical paths. (credit: NASA Blueshift, Flickr)

**periapsis**is the point at which the two objects are closest, and the

**apoapsis**is the point at which they are farthest apart. Generally, the velocity of the orbiting body tends to increase as it approaches the periapsis and decrease as it approaches the apoapsis. Some objects reach an escape velocity, which results in an infinite orbit. These bodies exhibit either a parabolic or a hyperbolic orbit about a body; the orbiting body breaks free of the celestial body’s gravitational pull and fires off into space. Each of these orbits can be modeled by a conic section in the polar coordinate system.

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- Precalculus.
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