Conic Sections Dr. Shildneck Fall, 2015

Conic Sections A conic section (or conic) is the intersection of a plane and a double-napped cone. There are four basic conic sections that we will study. The Circle The Ellipse The Parabola The Hyperbola

Degenerate Conics When a plane passes through the vertex of a double-napped cone, three special conics are created. Circle Ellipse Parabola Hyperbola Intersecting Lines Line Point

CONIC SECTIONS Circles

Circles Definition A circle is a locus of points such that every point is equidistant from a fixed point, called the center. Locus – a set of points that follow a general rule

Circles Standard Equation (x-h)2 + (y-k)2 = r2 h = x-coordinate of the center k = y-coordinate of the center r = radius of the circle

Example (x+4)2 + (y-2)2 = 25 Quick Graphs Find and Plot Center Find Radius Plot points to the top, bottom, right and left of center. Sketch a circle through those four points. Example (x+4)2 + (y-2)2 = 25

Writing Equations Know the standard form of the equation Often it helps if you sketch the curve described Find any critical values needed for the equation Plug those into the equation

Example: Write the equation of the circle shown.

Examples Write the equation of the circle with the following characteristics. Center (-3, 0) and radius 2 2 Center (5, -4) passing through (8, 8) With diameter running between (-2, 4) and (7, 9)

Assignment Alternate Text (on website) P. 667 Vocabulary #1-3 Exercises #1, 3, 5, 7, 9, 11, 21, 29, 31, 33, 35