[PDF] MATHEMATICS FORMULA BOOKLET - GYAAN SUTRA - Resonance PDF (969)-maths-gyaan-sutra-jee-main.pdf

Fundamental of Mathematics Statistics 47 – 49 23 Mathematical Reasoning 49 – 50 24 Sets and Relation Standard equation of the hyperbola is 1 2b

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[PDF] MATHEMATICS FORMULA BOOKLET - GYAAN SUTRA - Resonance

Fundamental of Mathematics Statistics 47 – 49 23 Mathematical Reasoning 49 – 50 24 Sets and Relation Standard equation of the hyperbola is 1 2b

[PDF] Mathematics & Statistics (40) - (AEJC), Mumbai

Mathematics is the language of all equations of standard equation, Conics of some standard functions, rules of integration 10 Statistics Measures of

Page # 1

S.No.Topic Page No.

1.Straight Line2 - 3

2.Circle4

3.Parabola5

4.Ellips5 -6

5.Hyperbola6 - 7

6.Limit of Function8 - 9

7.Method of Differentiation9 - 11

8.Application of Derivatves11 - 13

9.Indefinite Intedration14 - 17

10.Definite Integration17 - 18

11.Fundamental of Mathematics19 - 21

12.Quadratic Equation22 - 24

13.Sequence & Series24 - 26

14.Binomial Theorem26 - 27

15.Permutation & Combinnation28 - 29

16.Probability29 - 30

17.Complex Number31 - 32

18.Vectors32 - 35

19.Dimension35 - 40

20.Solution of Triangle41 - 44

21.Inverse Trigonometric Functions44 - 46

22.Statistics47 - 49

23.Mathematical Reasoning49 - 50

24.Sets and Relation50 - 51

INDEX

MATHEMATICS

FORMULA BOOKLET - GYAAN SUTRA

Page # 2

MATHEMATICS

FORMULA BOOKLET - GYAAN SUTRA

STRAIGHT LINE

1.Distance Formula:

2 2

1 2 1 2d (x - x ) (y - y ) .

2.Section Formula :

x = nm xnxm12 ; y = nm ynym12

3.Centroid, Incentre & Excentre:

Centroid G

3 yyy,3 xxx321321,

Incentre I

cba cybyay,cba cxbxax321321

Excentre I1

cba cybyay,cba cxbxax321321

4.Area of a Triangle:

ABC = 1yx 1yx 1yx 2 1 33
22
11

5.Slope Formula:

Line Joining two points (x1 y1) & (x2 y2), m =

21
21
xx yy

6.Condition of collinearity of three points:

1yx 1yx 1yx 33
22
11 = 0

7.Angle between two straight lines :

tan = 21
21
mm1 mm

Page # 3

8.Two Lines :

ax + by + c = 0 and ax + by + c = 0 two lines

1. parallel if a

a =b b c c

2. Distance between two parallel lines = 22

21
ba cc

3 Perpendicular : If aa + bb = 0.

9.A point and line:

1. Distance between point and line = axbyc

ab 11 22

2. Reflection of a point about a line:

22
1111
ba cbyax2b yy a xx

3. Foot of the perpendicular from a point on the line is

22
1111
ba cbyax b yy a xx

10.Bisectors of the angles between two lines:

22ba
cybxa 22ba
cybxa

11.Condition of Concurrency :

of three straight lines aix+ biy + ci = 0, i = 1,2,3 is abc abc abc 111
222
333
= 0.

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 = ba bah22

Page # 4

CIRCLE

1.Intercepts made by Circle x2 + y2 + 2gx + 2fy + c = 0 on the Axes:

(a) 2cg2 on x -axis(b) 2cf2 on y - aixs

2.Parametric Equations of a Circle:

x = h + r cos ; y = k + r sin

3.Tangent :

(a) Slope form : y = mx ± 2m1a (b) Point form : xx1 + yy1 = a2 or T = o (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 is1S

6.Director Circle: x2 + y2 = 2a2 for x2 + y2 = a2

7.Chord of Contact: T = 0

1. Length of chord of contact =22LR

RL2

2. Area of the triangle formed by the pair of the tangents & its chord of

contact = 22 3 LR LR

3. Tangent of the angle between the pair of tangents from (x1, y1)

22RL
LR2

4. Equation of the circle circumscribing the triangle PT1 T2 is :

(x x1) (x + g) + (y y1) (y + f) = 0.

8.Condition of orthogonality of Two Circles: 2 g1 g2 + 2 f1 f2 = c1 + c2.

9.Radical Axis : S1 S2 = 0 i.e. 2 (g1 g2) x + 2 (f1 f2) y + (c1 c2) = 0.

10.Family of Circles: S1 + K S2 = 0, S + KL = 0.

Page # 5

PARABOLA

1.Equation of standard parabola :

y2 = 4ax, Vertex is (0, 0), focus is (a, 0), Directrix is x + a = 0 and Axis is y = 0. Length of the latus rectum = 4a, ends of the latus rectum are L(a, 2a) & L' (a, 2a).

2.Parametric Representation: x = at² & y = 2at

3.Tangents to the Parabola y² = 4ax:

1. Slope form y = mx +m

a (m 0)2. Parametric form ty = x + at2

3. Point form T = 0

4.Normals to the parabola y² = 4ax :

y y1 =a2 y1 (x x1) at (x1, y1) ; y = mx 2am am3 at (am2 2am) ; y + tx = 2at + at3 at (at2, 2at).

ELLIPSE

1.Standard Equation : 2

2 2 2 b y a x = 1, where a > b & b² = a² (1 e²).

Eccentricity: e =2

2 a b1, (0 < e < 1), Directrices : x = ± e a. Focii : S (± a e, 0). Length of, major axes = 2a and minor axes = 2b

Vertices : A ( a, 0) & A (a, 0) .

Latus Rectum : = 22

e1a2a b2

2.Auxiliary Circle : x² + y² = a²

3.Parametric Representation : x = a cos & y = b sin

4.Position of a Point w.r.t. an Ellipse:

The point P(x1, y1) lies outside, inside or on the ellipse according as; 1b y a x 2 21
2

21 > < or = 0.

Page # 6

5.Line and an Ellipse:

The line y = mx + c meets the ellipse 2

2 2 2 b y a x = 1 in two points real, coincident or imaginary according as c² is < = or > a²m² + b².

6.Tangents:

Slope form: y = mx ± 222bma, Point form : 1b

yy a xx 2 1 2 1,

Parametric form: 1b

siny a cosx

7.Normals:

1 2 1 2 y yb x xa = a² b², ax. sec by. cosec = (a² b²), y = mx 222
22
mba mba

8.Director Circle: x² + y² = a² + b²

HYPERBOLA

1.Standard Equation:

Standard equation of the hyperbola is12b

2y 2a

2x, where b2 = a2 (e2 1).

Focii :S (± ae, 0) Directrices : x = ± a

Vertices : A (± a, 0)

Latus Rectum ( ) : = a

b22 = 2a (e2 1).

2.Conjugate Hyperbola :

1b y a x 2 2 2 2 & 1b y a x 2 2 2 2 are conjugate hyperbolas of each.

3.Auxiliary Circle : x2 + y2 = a2.

4.Parametric Representation : x = a sec & y = b tan

Page # 7

5.Position of A Point 'P' w.r.t. A Hyperbola :

S1 1b y a x 2 2 1 2 2

1 >, = or < 0 according as the point (x1, y1) lies inside, on

or outside the curve.

6.Tangents :

(i)Slope Form : y = m x222bma (ii)Point Form : at the point (x1, y1) is 1b yy a xx 2 1 2 1. (iii)Parametric Form : 1b anty a secx.

7.Normals :

(a)at the point P (x1, y1) is 1 2 1 2 y yb x xa = a2 + b2 = a2 e2. (b)at the point P (a sec , b tan ) is tan yb sec xa = a2 + b2 = a2 e2. (c)Equation of normals in terms of its slope 'm' are y = mx 222
22
mba mba

8.Asymptotes : 0b

y a x and0b y a x.

Pair of asymptotes :0b

y a x 2 2 2 2

9.Rectangular Or Equilateral Hyperbola : xy = c2, eccentricity is2.

Vertices : (± c, ±c) ; Focii :c2,c2. Directrices : x + y = c2

Latus Rectum (l ) : = 22 c = T.A. = C.A.

Parametric equation x = ct, y = c/t, t R - {0}

Equation of the tangent at P (x1

, y1) is 11y y x x = 2 & at P (t) is t x+ t y = 2 c. Equation of the normal at P (t) is x t3 y t = c (t4 1). Chord with a given middle point as (h, k) is kx + hy = 2hk.

Page # 8

quotesdbs_dbs8.pdfusesText_14

[PDF] [PDF] MATHEMATICS FORMULA BOOKLET - GYAAN SUTRA - Resonance

Page # 1

S.No.Topic Page No.

1.Straight Line2 - 3

2.Circle4

3.Parabola5

4.Ellips5 -6

5.Hyperbola6 - 7

6.Limit of Function8 - 9

7.Method of Differentiation9 - 11

8.Application of Derivatves11 - 13

9.Indefinite Intedration14 - 17

10.Definite Integration17 - 18

11.Fundamental of Mathematics19 - 21

12.Quadratic Equation22 - 24

13.Sequence & Series24 - 26

14.Binomial Theorem26 - 27

15.Permutation & Combinnation28 - 29

16.Probability29 - 30

17.Complex Number31 - 32

18.Vectors32 - 35

19.Dimension35 - 40

20.Solution of Triangle41 - 44

21.Inverse Trigonometric Functions44 - 46

22.Statistics47 - 49

23.Mathematical Reasoning49 - 50

24.Sets and Relation50 - 51

MATHEMATICS

FORMULA BOOKLET - GYAAN SUTRA

Page # 2

MATHEMATICS

FORMULA BOOKLET - GYAAN SUTRA

STRAIGHT LINE

1.Distance Formula:

1 2 1 2d (x - x ) (y - y ) .

2.Section Formula :

3.Centroid, Incentre & Excentre:

Centroid G

Incentre I

Excentre I1

4.Area of a Triangle:

5.Slope Formula:

Line Joining two points (x1 y1) & (x2 y2), m =

6.Condition of collinearity of three points:

7.Angle between two straight lines :

Page # 3

8.Two Lines :

1. parallel if a

2. Distance between two parallel lines = 22

3 Perpendicular : If aa + bb = 0.

9.A point and line:

1. Distance between point and line = axbyc

2. Reflection of a point about a line:

3. Foot of the perpendicular from a point on the line is

10.Bisectors of the angles between two lines:

11.Condition of Concurrency :

12.A Pair of straight lines through origin:

Page # 4

CIRCLE

1.Intercepts made by Circle x2 + y2 + 2gx + 2fy + c = 0 on the Axes:

2.Parametric Equations of a Circle:

3.Tangent :

4.Pair of Tangents from a Point: SS1 = T².

5.Length of a Tangent : Length of tangent is1S

6.Director Circle: x2 + y2 = 2a2 for x2 + y2 = a2

7.Chord of Contact: T = 0

1. Length of chord of contact =22LR

2. Area of the triangle formed by the pair of the tangents & its chord of

3. Tangent of the angle between the pair of tangents from (x1, y1)

4. Equation of the circle circumscribing the triangle PT1 T2 is :

8.Condition of orthogonality of Two Circles: 2 g1 g2 + 2 f1 f2 = c1 + c2.

9.Radical Axis : S1 S2 = 0 i.e. 2 (g1 g2) x + 2 (f1 f2) y + (c1 c2) = 0.

10.Family of Circles: S1 + K S2 = 0, S + KL = 0.

Page # 5

PARABOLA

1.Equation of standard parabola :

2.Parametric Representation: x = at² & y = 2at

3.Tangents to the Parabola y² = 4ax:

1. Slope form y = mx +m

3. Point form T = 0