Short notea

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

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, MATHEMATICS
FORMULA BOOKLET - GYAAN SUTRA
STRAIGHT LINE
1. Distance Formula:

d  (x1 – x2 )2  (y1 – y2 )2 .
2. Section Formula :
mx 2  nx1 my 2  ny1
x= ;y= .
mn mn
3. Centroid, Incentre & Excentre:

 x1  x 2  x 3 y1  y 2  y 3 
Centroid G  , ,
 3 3 

 ax1 bx 2  cx 3 ay1 by 2  cy 3 
Incentre I  , 
 abc a  b c 

  ax1  bx 2  cx 3  ay1  by 2  cy 3 
Excentre I1  , 
 abc abc 
4. Area of a Triangle:
x1 y1 1
1
 ABC = 2 x 2 y2 1
x3 y3 1
5. Slope Formula:
y1  y 2
Line Joining two points (x1 y1) & (x2 y2), m =
x1  x 2
6. Condition of collinearity of three points:
x1 y1 1
x2 y2 1 = 0
x3 y3 1
7. Angle between two straight lines :
m1  m 2
tan  = .
1  m1m 2
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,8. Two Lines :
ax + by + c = 0 and ax + b y + c  = 0 two lines

a b c
1. parallel if =  .
a b c

c 1 c 2
2. Distance between two parallel lines = .
a 2 b 2
3 Perpendicular : If aa + bb  = 0.
9. A point and line:

a x1  b y 1  c
1. Distance between point and line = .
a 2  b2
2. Reflection of a point about a line:

xx1 yy1 ax 1  by 1  c
 2
a b a 2 b 2
3. Foot of the perpendicular from a point on the line is
x  x1 y  y1 ax 1by1 c
  
a b a 2 b 2
10. Bisectors of the angles between two lines:
ax  by  c ax  by  c 
=±
2 2
a b a 2  b2
11. Condition of Concurrency :

a1 b1 c1
of three straight lines ai x+ b i y + c i = 0, i = 1,2,3 is a 2 b2 c 2 = 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 h 2  ab
= .
ab

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, CIRCLE
1. Intercepts made by Circle x2 + y2 + 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 : xx1 + yy1 = a2 or T = o
(c) Parametric form : x cos  + y sin  = a.

4. Pair of Tangents from a Point: SS 1 = T².

5. Length of a Tangent : Length of tangent is S1

6. Director Circle: x2 + y2 = 2a2 for x2 + y2 = a2
7. Chord of Contact: T = 0
2 LR
1. Length of chord of contact =
R 2  L2
2. Area of the triangle formed by the pair of the tangents & its chord of

R L3
contact =
R 2  L2
3. Tangent of the angle between the pair of tangents from (x1, y1)

 2R L 
=  2

2 
 L  R 
4. Equation of the circle circumscribing the triangle PT 1 T 2 is :
(x  x1) (x + g) + (y  y1) (y + f) = 0.

8. Condition of orthogonality of Two Circles: 2 g 1 g 2 + 2 f1 f2 = c 1 + c 2.
9. Radical Axis : S 1  S 2 = 0 i.e. 2 (g 1  g 2) x + 2 (f1  f2) y + (c 1  c 2) = 0.

10. Family of Circles: S 1 + K S 2 = 0, S + KL = 0.


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