Conics Formula Sheet - Download as DOC

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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)
radius: r
                                                                                                       2        2

				
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