Intro to Conics
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Introduction to Conic Sections
A conic section is a curve formed by the intersection of _________________________
a plane and a double cone.
(h , k)
r
The set of all points that are the same distance from the center.
Standard Equation:
With CENTER: (h, k)
& RADIUS: r (square root)
®

h
,
)
(
2
8
h
r²
k
Center:
Radius: r 9
(
)
k
,
Center ?
Radius ?
Standard Equation:
(h , k)
a
b
Basically an ellipse is a squishedcircle
Center: (h , k)
a: major radius (horizontal), length from center to edge of circle
b: minor radius (vertical), length from center to top/bottom of circle
* You must square root the denominator
This must equal 1
a²
b
2
Center: (4 , 5)
a: 5
b: 2
Standard Equations:
OR
vertex
vertex
We’ve talked about this before…
a Ushaped graph
This equation opens left or right
This equation opens up or down
HOW DO YOU TELL…LOOK FOR THE SQUARED VARIABLE
Example 5
opens down
What is the vertex?How does it open?
(2 , 5)
opens right
What is the vertex?How does it open?
(0 , 2)
Standard Equations:
OR
What I look like…two parabolas, back to back.
This equation opens up and down
This equation opens left and right
Have I seen this before? Sort of…only now we have a minus sign in the middle
(h , k)
Center: (h , k)
Center: (4 , 5)
Opens: Left and right
What am I?
Name the conic section and its center or vertex.
circle; (0,0)
hyperbola; (0,0)
parabola; vertex (1,2)
parabola; vertex (2,3)
circle; (2,0)
ellipse; (0,0)
hyperbola; (1,2)
circle; (2,1)
hyperbola; (5,7)
parabola; vertex (0,0)
hyperbola; (0,1)
ellipse; (5,4)