CONICS Parabola V D: x = –a F = (a, 0) x y = y ax 4 2 V D: x = a F = (–a, 0) x y = − y ax 4 2 V D: y = –a F = (0, a) x y = x ay 4 2 x y V F = (0, –a) D: y = a = − x ay 4 2 Ellipse (0, b) (0, –b) F1 = (–c, 0) V1 = (–a, 0) V 2 = (a, 0) F2 = (c, 0) x y + = > = − x a y b a b c a b 1, , 2 2 2 2 2 2 2 F2 = (0, c) (b, 0) (–b, 0) F1 = (0, –c) V2 = (0, a) V1 = (0, –a) x y + = > = − x b y a a b c a b 1, , 2 2 2 2 2 2 2 F2 = (c, 0) F1 = (–c, 0) V2 = (a, 0) V1 = (–a, 0) x y − = = + x a y b c a b 1, 2 2 2 2 2 2 2 Asymptotes: = = − y b a x y b a x , V1 = (0, –a) V2 = (0, a) F2 = (0, c) F1 = (0, –c) x y − = = + y a x b c a b 1, 2 2 2 2 2 2 2 Asymptotes: = = − y a b x y a b x , Hyperbola PROPERTIES OF LOGARITHMS ( ) = + MN M N log log log a a a ( ) = − M N M N log log log a a a = M r M log log a r a = = M M a M a log log log ln ln a a e x x a ln = PERMUTATIONS/COMBINATIONS = 0! 1 = 1! 1 n n n ! 1 ... 321 ( ) ( )( )( ) = − ⋅ ⋅ ( ) ( ) = − P n r n n r , ! ! ( ) ( ) = ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = − C n r n r n n r r , ! ! ! BINOMIAL THEOREM ( ) + = + ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ + ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ + + − ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ + − − − a b a n ba n b a n n b a b 1 2 . . . 1 n n n n n n 1 2 2 1 ARITHMETIC SEQUENCE a a d a d a n d n a n d n a a 2 . . . 1 2 2 1 2 n 1 1 1 1 1 1 [ ] ( ) ( ) [ ] [ ] ( ) ( ) + + + + + + + − = + − = + GEOMETRIC SEQUENCE + + + + = ⋅ − − − a a r a r a r a r r . . . 1 1 n n 1 1 1 2 1 1 1 GEOMETRIC SERIES r a a r a r a r a r If 1, . . . 1 k k 1 1 1 2 1 1 1 1 ∑ < + + + = = − = ∞ −
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