Notes - Introduction to Conic Sections
Do Play Doh Activity slicing
cone into different conic
sections.
(See Calculus in Motion: Conics Definitions and Graphs)
Look at Geo Sketchpad simulations for
conic sections.
Standard Form for Each Equation
Circle
Parabola
(x - h)2 + (y - k)2 = r2
y = a(x - h)2 + k
x = a(y - k)2 + h
Ellipse
Hyperbola
(x - h)2 + (y - k)2 = 1
a
2
b
2
(x - h)2
a2
(y - k)2
a2
For all, center is at (h,k)
(y - k)2 = 1
b2
(x - h)2 = 1
b2
Identifying Conics
To classify a conic from its general equation:
The graph of
is one of the following.
1.
2.
3.
4.
Circle:
Parabola:
Ellipse:
Hyperbola:
A=C
AC = 0
AC > 0
AC < 0
OR you can complete the square for the x and y terms to determine the standard form of the conic.
EX: Classify the graph of each equation. Use the guidelines above OR complete the square.