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Allan Danuff
Building 7, Room 102D
(352) 854-2322, Ext. 1262

Conic Sections

Parabola:


Vertex: ( h, k )


Direction: p>0 up, p<0 down

Focus: ( h, k + p )

Directrix: y = k – p

Vertex: ( h, k )


Direction: p>0 right, p<0 left

Focus: ( h + p, k )

Directrix: x = h - p

 

Circle:

 

Center: ( h, k ) 

Radius: r

 

Ellipse:

 

 

If a > b:  

Center: ( h, k )


Major Vertices:
( h + a, k), ( h – a, k)

Minor Vertices:
( h, k + b), ( h, k – b)

Foci:
( h + c, k ), ( h – c, k )

If a < b:  

Center: ( h, k )


Major Vertices:
( h, k + b), ( h, k – b)

Minor Vertices:
( h + a, k), ( h - a, k)

Foci:
( h, k + c ), ( h, k – c )

 

Hyperbola:

 

 

Vertices:

( h + a, k ), ( h - a, k ) 


Asymptotes: 

Foci : 


( h + c, k ), ( h – c, k )

 

Vertices:

( h , k + b ), ( h , k - b ) 


Asymptotes: 

Foci :


( h, k + c ), ( h, k - c )


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