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Intro to Conics

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

a plane and a double cone.

(h , k) _________________________

r

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

Standard Equation:

With CENTER: (h, k)

& RADIUS: r (square root)

Standard Equation: _________________________

(h , k)

a

b

EllipseBasically 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

Standard Equations: _________________________

OR

vertex

Parabolavertex

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 4opens 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

HyperbolasWhat 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)

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) _________________________

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