Page 3 - For Okta_Float

10-2

Circles

OBJECTIVES
• Use and Real World SEISMOLOGY Portable autonomous digital seismographs (PADSs)
determine the Application are used to investigate the strong ground motions produced by the
standard and aftershocks of large earthquakes. Suppose a PADS is deployed 2 miles
general forms west and 3.5 miles south of downtown Olympia, Washington, to record the aftershocks
of the equation
of a circle. of a recent earthquake. While there, the PADS detects and records the seismic activity
of another quake located 24 miles away. What are all the possible locations of this
• Graph circles.
earthquake’s epicenter? This problem will be solved in Example 2.

The pattern of the shock waves from an earthquake form concentric circles.
A circle is the set of all points in the plane that are equidistant from a given point
radius in the plane, called the center. The distance from the center to any point on the
center circle is called the radius of the circle. Concentric circles have the same center
but not necessarily the same radius.

A circle is one type of conic section. Conic sections, which include circles,
parabolas, ellipses and hyperbolas, were first studied in ancient Greece sometime
between 600 and 300 B.C. The Greeks were largely concerned with the properties,
not the applications, of conics. In the seventeenth century, applications of conics
became prominent in the development of calculus.
Conic sections are used to describe all of the possible ways a plane and a
double right cone can intersect. In forming the four basic conics, the plane does
not pass through the vertex of the cone.

circle ellipse parabola hyperbola
When the plane does pass through the vertex of a conical surface, as
illustrated below, the resulting figure is called a degenerate conic. A degenerate
conic may be a point, line, or two intersecting lines.

point line intersecting lines
(degenerate ellipse) (degenerate parabola) (degenerate hyperbola)
Lesson 10-2 Circles 623