MATHEMATICS
               FORMULA BOOKLET - GYAAN SUTRA
                                           INDEX
                 S.No.       Topic                                   Page No.
                 1.      Straight Line                           2 – 3
                 2.      Circle                                  4
                 3.      Parabola                                5
                 4.      Ellips                                  5 –6
                 5.      Hyperbola                               6 – 7
                 6.      Limit of Function                       8 – 9
                 7.      Method of Differentiation               9 – 11
                 8.      Application of Derivatves               11 – 13
                 9.      Indefinite Intedration                  14 – 17
                 10.     Definite Integration                    17 – 18
                 11.     Fundamental of Mathematics              19 – 21
                 12.     Quadratic Equation                      22 – 24
                 13.     Sequence & Series                       24 – 26
                 14.     Binomial Theorem                        26 – 27
                 15.     Permutation & Combinnation              28 – 29
                 16.     Probability                             29 – 30
                 17.     Complex Number                          31 – 32
                 18.     Vectors                                 32 – 35
                 19.     Dimension                               35 – 40
                 20.     Solution of Triangle                    41 – 44
                 21.     Inverse Trigonometric Functions         44 – 46
                 22.     Statistics                              47 – 49
                 23.     Mathematical Reasoning                  49 – 50
                 24.     Sets and Relation                       50 – 51
                                                                               Page # 1
                                      MATHEMATICS
                FORMULA BOOKLET - GYAAN SUTRA
                                     STRAIGHT LINE
         1.       Distance Formula:
                                  2           2 .
                   d (x –x ) (y –y )
                           1    2      1    2
         2.       Section Formula :
                  x =  mx2nx1  ; y = my2ny1 .
                         mn              mn
         3.       Centroid, Incentre & Excentre:
                                x1  x2  x3 , y1  y2  y3 
                  Centroid G         3             3        ,
                                                           
                             ax bx cx       ay by cy 
                                 1     2    3     1    2     3
                  Incentre I                 ,                
                                 abc           abc        
                                                              
                                ax1bx2cx3 ay1by2cy3 
                  Excentre  I                    ,                 
                             1    abc             abc        
                                                                   
         4.       Area of a Triangle:
                            1 x1    y1  1
                   ABC = 2 x2 y2 1
                               x3  y3 1
         5.       Slope Formula:
                  Line Joining two points (x  y ) & (x  y ), m =  y1y2
                                             1 1      2 2        x1x2
         6.       Condition of collinearity of three points:
                    x1   y1   1
                    x2   y2 1  = 0
                    x3   y3 1
         7.       Angle between two straight lines :
                           m m
                  tan  =    1    2 .
                          1m m
                                1 2
                                                                                       Page # 2
          8.        Two Lines :
                    ax + by + c = 0 and ax + by + c = 0 two lines
                    1. parallel if   a  = b    c .
                                  a           
                                        b      c
                    2. Distance between two parallel  lines  =         c1c2     .
                                                                        a2b2
                    3 Perpendicular : If aa + bb = 0.
          9.        A point and line:
                    1. Distance between point and line =  ax1  by1  c .
                                                                     a2 b2
                    2. Reflection of a point about a line:
                               x  x 1  y  y 1   2 ax 1  by 1  c
                                  a           b                a 2  b 2
                    3. Foot of the perpendicular from a point on the line is
                              xx1     yy1       ax1by1c
                                a    b            a2b2
          10.       Bisectors of the angles between two lines:
                              axbyc                       
                                            = ±  a x  b y  c
                                 a2b2                2     2
                                                    a b
          11.       Condition of Concurrency :
                                                                           a     b    c
                                                                             1    1     1
                    of three straight lines aix+ biy + ci = 0, i = 1,2,3 is a2   b2   c2  = 0.
                                                                           a3    b3   c3
          12.       A Pair of straight lines through origin:
                                
                    ax²+ 2hxy+ by² = 0
                    If  is the acute angle between the pair of straight lines, then tan 
                       2 h2ab
                    =     ab      .
                                                                                             Page # 3
                                                                                    CIRCLE
                                                                                                2       2 
                 1.               Intercepts made by Circle x + y + 2gx + 2fy + c = 0 on the Axes:
                                  (a) 2        g2c  on x -axis                     (b) 2        f 2c   on y - aixs
                 2.               Parametric Equations of a Circle:
                                  x = h + r cos  ;  y = k + r sin 
                 3.               Tangent :
                                  (a) Slope form :  y = mx ± a                              1m2
                                  (b) Point form :  xx  + yy  = a2 or T = o
                                                                       1         1
                                  (c) Parametric form :                             x cos  + y sin  = a.
                 4.               Pair of Tangents from a Point: SS1 = T².
                 5.               Length of a Tangent : Length of tangent is S1
                                                                        2       2          2          2       2        2
                 6.               Director Circle: x  + y  = 2a  for x  + y  = a
                 7.               Chord of Contact: T = 0
                                  1. Length of chord of contact =                                 2LR
                                                                                                     2       2
                                                                                                  R L
                                  2. Area of the triangle formed by the pair of the tangents & its chord of
                                                              3
                                  contact =  RL
                                                         2       2
                                                      R L
                                  3. Tangent of the angle between the pair of tangents from (x , y )
                                                                                                                                                       1      1
                                                                        2RL 
                                                                   =  2             2 
                                                                       L R 
                                                                                        
                                  4. Equation of the circle circumscribing the triangle PT1 T2 is :
                                                                   (x  x ) (x + g) + (y  y ) (y + f) = 0.
                                                                             1                              1
                 8.               Condition of orthogonality of Two Circles:  2 g g + 2 f f  = c + c .
                                                                                                                                           1   2         1  2        1      2
                 9.               Radical Axis : S   S  = 0  i.e. 2 (g  g ) x + 2 (f  f ) y + (c  c ) = 0.
                                                                      1        2                        1       2                1      2              1       2
                 10.              Family of Circles:  S1 + K S2 = 0, S + KL = 0.
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