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# Intro to Conics - PowerPoint PPT Presentation

Intro to Conics

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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

### Circles

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

-k

Center:

Radius: r 9

(

)

k

,

### Example 2

Center ?

Radius ?

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

This must equal 1

b

### Example 3

2

Center: (-4 , 5)

a: 5

b: 2

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 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)

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

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)