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Vocabulary
Complete the definitions.
Word  Definition 
Dandelin Spheres  __________________________________________________________________ 
Tangent  __________________________________________________________________ 
Ellipse  __________________________________________________________________ 
Parabola  __________________________________________________________________ 
Hyperbola  __________________________________________________________________ 
Conic Sections
Dandelin Spheres
In your own words, describe how Dandelin used spheres to find the foci and prove the focal property:
________________________________________________________________________
In your own words, describe how Morton used Dandelin Spheres to prove the focal property for parabolas:
________________________________________________________________________
Finally, in your own words, describe how Dandelin Spheres prove the focal property for hyperbolas:
________________________________________________________________________
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 If two tangents are drawn from a single point to a sphere, what can you say about the line segments formed
 What is the line that results from the intersection between the cutting plane and the plane that contains the circle of contact between the sphere and cone?
 What is defined by the point where the sphere intersects the cutting plane?
 How do the tangents relate to a radius of a sphere?

Identify the parts listed on the diagram as specified below:
 Directrix Line  Small Sphere
 Directrix Line  Large Sphere
 Focus  Small Sphere
 Focus  Large Sphere
 Vertex  Small Sphere
 Vertex  Large Sphere
 Directrix Plane  Small Sphere
 Directrix Plane  Large Sphere
 Cutting Plane
 What conic section is illustrated here?
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General Forms of Conic Sections
Complete the chart.
Conic Section  Properties  Equation 
Ellipse  _____________________________________________________  ____________________ 
Parabola  _____________________________________________________  ____________________ 
Hyperbola  _____________________________________________________  ____________________ 
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How can we look at a degree2 polynomial equation and determine which conic section it depicts?
If
if
if
.
Identify the conic that is represented by the equation.

(x−5)24+(y−4)24=1 
(x−3)2+y−22=1 
x2−5x−y2−4y+16=0

9x2+4y2−36x+64y+256=0 
9x2+y2+90x−8y+232=0 
9x2−9y2+162x+162y−81=0
Identify and Graph the following:

(x−1)24=(y)216=1 
x=2(y+2)2−1 
x=−(y−2)2+4
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