1. Conic Sections
Dr. Shildneck
Fall, 2015

2. 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

3. 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

4. CONIC SECTIONS
Circles

5. 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

6. 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

7. 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

8. 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

9. Example:
Write the equation of the circle shown.

10. 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)

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