Introduction to Conic Sections
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Intro to Conics

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Slide1 l.jpg

Introduction to Conic Sections


A conic section is a curve formed by the intersection of l.jpg

A conic section is a curve formed by the intersection of _________________________

a plane and a double cone.


Circles l.jpg

(h , k)

r

Circles

The set of all points that are the same distance from the center.

Standard Equation:

With CENTER: (h, k)

& RADIUS: r (square root)


Example 1 l.jpg

®

-

h

,

)

(

2

8

Example 1

-h

-k

Center:

Radius: r 9

(

)

k

,


Example 2 l.jpg

Example 2

Center ?

Radius ?


Ellipse l.jpg

Standard Equation:

(h , k)

a

b

Ellipse

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


Example 3 l.jpg

This must equal 1

b

Example 3

2

Center: (-4 , 5)

a: 5

b: 2


Parabola l.jpg

Standard Equations:

OR

vertex

Parabola

vertex

We’ve talked about this before…

a U-shaped graph

This equation opens left or right

This equation opens up or down

HOW DO YOU TELL…LOOK FOR THE SQUARED VARIABLE

  • Vertex: (h , k)

  • If there is a negative in front of the squared variable, then it opens down or left.

  • If there is NOT a negative, then it opens up or right.


Example 4 l.jpg

Example 5

Example 4

opens down

What is the vertex?How does it open?

(-2 , 5)

opens right

What is the vertex?How does it open?

(0 , 2)


Hyperbolas l.jpg

Standard Equations:

OR

Hyperbolas

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)


Example 6 l.jpg

Example 6

Center: (-4 , 5)

Opens: Left and right


Slide13 l.jpg

What am I?

Name the conic section and its center or vertex.


Slide14 l.jpg

circle; (0,0)


Slide15 l.jpg

hyperbola; (0,0)


Slide16 l.jpg

parabola; vertex (1,-2)


Slide17 l.jpg

parabola; vertex (-2,-3)


Slide18 l.jpg

circle; (2,0)


Slide19 l.jpg

ellipse; (0,0)


Slide20 l.jpg

hyperbola; (1,-2)


Slide21 l.jpg

circle; (-2,-1)


Slide22 l.jpg

hyperbola; (-5,7)


Slide23 l.jpg

parabola; vertex (0,0)


Slide24 l.jpg

hyperbola; (0,1)


Slide25 l.jpg

ellipse; (-5,4)


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