POINTS Preface 1 1. System of Co - ordinates 2 1.1 Cartesian Co-ordinates 1.2 Polar Co-ordinates 2. Distance Formula 2 3. Applications of Distance Formula 3 3.1 Position of three points 3.2 Position of four points 4. Section Formula 4 5. Co-ordinate of some particular points 4 5.1 Centroid 5.2 Incentre 5.3 Circumcentre 5.4 Ortho Centre 6. Area of triangle and quadrilateral 6 6.1 Area of Triangle 6.2 Area of Quadrilateral 7. Transformation of axes 7 7.1 Parallel Transformations 7.2 Rotational Transformation 7.3 Reflection of a Point 8. Locus 8 9. Some important points 9 10. Solved examples 10 STRAIGHT LINE Preface 13 1. Equation of Straight line 14 2. Equation of Straight line parallel to axes 14 3. Slope of a line 14 4. Different forms of the equation of straight line 14 4.1 Slope – Intercept Form 4.2 Slope Point Form 4.3 Two Point Form 4.4 Intercept Form 4.5 Normal Form 4.6 Parametric Form 5. Reduction of General form of Equations into Standard Forms 15 6. Position of a point relative to a line 17 7. Angle between two straight lines 17 7.1 Parallel lines 7.2 Perpendicular lines 7.3 Coincident lines 8. Equation of parallel & perpendicular lines 18 9. Equation of Straight lines through (x , y ) making an angle α with y = mx + c 18 10. Length of perpendicular 19 10.1 Distance between two Parallel Lines 11. Condition of concurrency 19 12. Bisectors of angles between two lines 20 13. Line passing through the point of intersection of two lines 20 14. Homogeneous equation 20 15. General Equation of Second degree 21 16. Equation of lines joining the intersection points of a line & a curve to the origin 21 17. Some important points 22 18. Solved examples 23 CIRCLE Preface 29 1. Definition 30 2. Standard Form of equation of a circle 31 2.1 General Form 2.2 Central Form 2.3 Diametral Form 2.4 Parametric Form 3. Equation of a circle in some special cases 31 4. Position of a point with respect to a circle 32 4.1 The least and the greatest distance of a point from a circle 5. Line and circle 33 5.1 Condition of Tangency 5.2 Intercepts made on coordinate axes by the circle 6. Equation of tangent and normal 34 6.1 Equation of Tangent 6.2 Equation of Normal 6.3 Length of Tangent 6.4 Pair of Tangents 7. Chord of contact 35 8. Director circle 35 9. Position of two circles 36 10. Equation of a chord whose middle point is given 38 11. Circle through the point of intersection 38 12. Common chord of two circles 39 13. Angle of intersection of two circles 39 14.1 Condition of Orthogonality 14. Some important points 40 15. Pole and Polar 40 9.1 Equation of Polar 9.2 Co-ordinates of Pole 9.3 Conjugate Points and Conjugate Lines 16. Radical axis and radical centre 41 16.1 Radical Axis 16.2 Radical Centre 17. Solved examples 42 PARABOLA Preface 50 1. Definition 51 2. Terms related to parabola 51 3. Standard form of equation of parabola 51 3.1 Parameters of the Parabola y2 = 4ax 3.2 Other Standard Parabola 4. Reduction to Standard Equation 53 . 5. General equat

1. CONTENTS
POINTS
TOPIC PAGE NO.
Preface .................................................................................................................................................... 1
1. System of Co - ordinates ................................................................................................................... 2
1.1 Cartesian Co-ordinates
1.2 Polar Co-ordinates
2. Distance Formula .................................................................................................................................. 2
3. Applications of Distance Formula ....................................................................................................... 3
3.1 Position of three points
3.2 Position of four points
4. Section Formula..................................................................................................................................... 4
5. Co-ordinate of some particular points ....................................................................................... 4
5.1 Centroid
5.2 Incentre
5.3 Circumcentre
5.4 Ortho Centre
6. Area of triangle and quadrilateral ............................................................................................. 6
6.1 Area of Triangle
6.2 Area of Quadrilateral
7. Transformation of axes ......................................................................................................................... 7
7.1 Parallel Transformations
7.2 Rotational Transformation
7.3 Reflection of a Point
8. Locus ........................................................................................................................................................ 8
9. Some important points.......................................................................................................................... 9
10. Solved examples ................................................................................................................................... 10
STRAIGHT LINE
TOPIC PAGE NO.
Preface .................................................................................................................................................... 13
1. Equation of Straight line ...........................................................................................................14
2. Equation of Straight line parallel to axes .................................................................................... 14
3. Slope of a line .............................................................................................................................14

2. CIRCLE
TOPIC PAGE NO.
Preface .................................................................................................................................................... 29
1. Definition ................................................................................................................................................. 30
2. Standard Form of equation of a circle .......................................................................................... 31
2.1 General Form
2.2 Central Form
2.3 Diametral Form
2.4 Parametric Form
3. Equation of a circle in some special cases ....................................................................................... 31
4. Different forms of the equation of straight line.......................................................................... 14
4.1 Slope – Intercept Form
4.2 Slope Point Form
4.3 Two Point Form
4.4 Intercept Form
4.5 Normal Form
4.6 Parametric Form
5. Reduction of General form of Equations into Standard Forms ................................................. 15
6. Position of a point relative to a line........................................................................................... 17
7. Angle between two straight lines ....................................................................................................... 17
7.1 Parallel lines
7.2 Perpendicular lines
7.3 Coincident lines
8. Equation of parallel & perpendicular lines ....................................................................................... 18
9. Equation of Straight lines through (x1
, y1
) making an angle  with y = mx + c .......................... 18
10. Length of perpendicular ............................................................................................................. 19
10.1 Distance between two Parallel Lines
11. Condition of concurrency ........................................................................................................... 19
12. Bisectors of angles between two lines ...................................................................................... 20
13. Line passing through the point of intersection of two lines ...................................................... 20
14. Homogeneous equation........................................................................................................................ 20
15. General Equation of Second degree.................................................................................................. 21
16. Equation of lines joining the intersection points of a line & a curve to the origin ................... 21
17. Some important points ............................................................................................................... 22
18. Solved examples ................................................................................................................................... 23

3. 4. Position of a point with respect to a circle ........................................................................................ 32
4.1 The least and the greatest distance of a point from a circle
5. Line and circle ............................................................................................................................ 33
5.1 Condition of Tangency
5.2 Intercepts made on coordinate axes by the circle
6. Equation of tangent and normal .............................................................................................. 34
6.1 Equation of Tangent
6.2 Equation of Normal
6.3 Length of Tangent
6.4 Pair of Tangents
7. Chord of contact ..................................................................................................................................... 35
8. Director circle ............................................................................................................................. 35
9. Position of two circles ................................................................................................................ 36
10. Equation of a chord whose middle point is given ..................................................................... 38
11. Circle through the point of intersection ..................................................................................... 38
12. Common chord of two circles .................................................................................................... 39
13. Angle of intersection of two circles............................................................................................ 39
14.1 Condition of Orthogonality
14. Some important points ............................................................................................................... 40
15. Pole and Polar ............................................................................................................................ 40
9.1 Equation of Polar
9.2 Co-ordinates of Pole
9.3 Conjugate Points and Conjugate Lines
16. Radical axis and radical centre ................................................................................................. 41
16.1 Radical Axis
16.2 Radical Centre
17. Solved examples ................................................................................................................................... 42
PARABOLA
TOPIC PAGE NO.
Preface........................................................................................................................................ 50
1. Definition................................................................................................................................ 51
2. Terms related to parabola.......................................................................................................51
3. Standard form of equation of parabola..................................................................................51
3.1 Parameters of the Parabola y2
= 4ax
3.2 Other Standard Parabola
4. Reduction to Standard Equation..............................................................................................53
.

4. ELLIPSE
TOPIC PAGE NO.
Preface.............................................................................................................................. 68
1. Definition .......................................................................................................................... 69
2. Equation of Ellipse ............................................................................................................ 69
2.1 Standard Form
Various parameters related to ellipse
2.2 General equation of an ellipse
(Condition) for general eq. of the second degree in xy Real ellipse
3. Parametric equation of ellipse........................................................................................... 71
5. General equation of a Parabola.............................................................................................54
6. Equation of Parabola when its vertex and focus are given....................................................54
7. Parametric equation of a Parabola........................................................................................55
8. Chord.................................................................................................................................... 55
8.1 Equation of Chord
8.2 Length of Intercept
9. Position of a point and a line with respect to a Parabola.....................................................56
9.1 Position of a Point with respect to a Parabola
9.2 Line and Parabola
10. Tangent to the Parabola ........................................................................................................56
10.1 Condition of Tangency
10.2 Equation of Tangent
11. Normal to the Parabola...........................................................................................................57
11.1 Equation of Normal
11.2 Properties of Normal
12. Pair of Tangents.....................................................................................................................59
12.1 Locus of point of intersection of tangents
13. Chord of Contact ...................................................................................................................59
14. Equation of the chord with given midpoint ...........................................................................60
.
15. Diameter of the parabola ......................................................................................................60
16. Geometrical properties of the parabola ................................................................................60
17. Solved Examples...................................................................................................................63

5. 4. Point and Ellipse ............................................................................................................... 71
5. Ellipse and Line................................................................................................................. 71
5.1 Equation of tangent
5.2 Equation of the normal
6. Equation of the pair of Tangents ....................................................................................... 73
7. Equation of the chord of contact ....................................................................................... 73
8. Equation of the Chord Joining mid- Point (X1
, Y1
)............................................................... 73
9. Diameter.............................................................................................................................73
10. Solved Examples ...............................................................................................................74
HYPERBOLA
TOPIC PAGE NO.
Preface............................................................................................................................. 79
1. Standard Equation & Definition .............................................................................................80
2. Conjugate Hyperbola ............................................................................................................80
3. Parametric equations of the Hyperbola.................................................................................. 81
4. Position of a Point P (X1
, Y1
) with respect to Hyperbola ........................................................82
5. Line and Hyperbola ..............................................................................................................82
6. Equation of tangent ..............................................................................................................82
7. Equation of Normal ...............................................................................................................83
8. Equation of Pair of Tangents ..................................................................................................83
9. Chord of contact......................................................................................................................84
10. Equation of a chord whose middle point is given .................................................................84
11. Director Circle ........................................................................................................................84
12. Solved Examples ...................................................................................................................85
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