1. Symmetry Every line through center
Ex 1) Write the equation given the center at (0,4) and a radius of 3.
Center: (h,k)
Radius: r
Symmetry Every line through center
Cone cut by a plane parallel to the base
Real World:
tunnels
(h,k) r

2. Circles Steps to graph Steps to write equation
Find center
Find radius
Plot center
Count left, right, up and down to plot points
Connect the 4 points with curve.
Steps to write equation
Find center
Find radius
Substitute into formula.
Ex 3) Write the equation given the graph
Ex 2) Graph
(x-2)2 + (y+3)2 = 16
Center: (2, -3)
Radius:
Center: (-1, 1)
Radius: 5
(x--1)2 + (y-1)2 = 52
(x+1)2 + (y-1)2 = 25
Circles

3. Cone cut by a plane at an angle through the sides
Hyperbola
Parabola
Ellipse
Cone cut by a plane at an angle through the sides
Real World:
Tunnels
Cone cut by a plane perpendicular to the base
Real World:
tunnels
Cone cut by a plane at an angle through the base and 1 side
Real World:
tunnels and overpasses