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```									                                     Conics Formula Sheet
Parabolas
Vertical                                                             Horizontal

y  a( x  h) 2  k                                                  x  a( y  k ) 2  h
vertex: (h, k)                                                       vertex: (h, k)
            1                                                              1   
focus:  h, k                                                      focus:  h          ,k
            4a                                                             4a 
1                                                                   1
directrix: y  k                                                    directrix: x  h 
4a                                                                  4a
1                                                                   1
latus rectum:                                                        latus rectum:
a                                                                   a
axis of symmetry : x = h                                             axis of symmetry: y = k

Ellipses
Horizontal                                                           Vertical

( x  h) 2        (y  k)2                                            ( x  h) 2       (y  k)2
                 1                                                       1
a2          b2                                                       b2          a2
(major axis is horizontal)                                           (major axis is vertical)

center: (h, k)                                                       center: (h, k)
c  a b2        2
c  a2  b2
foci: (h + c, k) and (h – c, k)                                      foci: (h, k + c) and (h, k – c)
vertices: (h + a, k ), (h – a, k)                                    vertices: (h, k + a) , (h, k – a)

Hyperbolas
Horizontal                                                           Vertical

( x  h) 2        (y  k)2                                            (y  k)2         ( x  h) 2
                 1                                                                 1
a2                b2                                                 a2               b2

center: (h, k)                                                       center: (h, k)
c  a b2        2
c  a2  b2
foci: (h + c, k) and (h – c, k)                                      foci: (h, k + c) and (h, k – c)
vertices: (h + a, k) and (h – a, k)                                  vertices: (h, k + a) and (h, k – a)
b                                                                     a
asymptotes: y  k   ( x  h)                                       asymptotes: y  k   ( x  h)
a                                                                     b

Circles                                                       Distance and Midpoint

( x  h) 2  ( y  k ) 2  r 2                                                                      x1  x 2 y1  y 2
d  ( x2  x1 ) 2  ( y 2  y1 ) 2                      (           ,         )
center: (h, k)