Category: Coordinate Geometry / IIT JEE MAINS/ADVANCED-FREE STUDY MATERIAL

Contains concepts and problems related to straight lines , circles,parabola,ellipse,hyperbola
It contains straight lines,circle,parabola , ellipse,hyperbola,Concepts and Solved example at JEE Mains/advanced level

STRAIGHT LINES
Concepts – 1
1.1 (i) Distance in Rectangular
(ii) Area of Triangles
(iii) Area of Quadrilateral
1.2 (i) Slope of Lines
(ii) Equations of Lines
(iii) Angle Between Lines
(iv) Equation of lines making given angle with
another
1.3 (i) Condition of collinearity for three points (ii) Concurrency of lines
P1 – Solved Problems

P2-CONCEPTS
2.1 (i) Position of point with respect to line
2.2 (i) Parametric equation of lines
(ii) length of perpendicular
(iii) Foot, image of point
(iv) Distance between parallel lines
(v) area of parallelogram
2.3 (i) Section formula n its converse
(ii) Division By A Line
(iii) pmt n its application

P2-solved problem

P3-CONCEPTS
3.1 (i) family of lines
(ii) equations of diagonals of parallelogram
3.2 (i) concept of angular bisectors acute,obtuse
(ii) containing given point or not.
3.3 Solving skills of max min type problems
P3- Solved problems

P4- CONCEPTS
4.1 (i) how we get reflected ray when incident ray is
given
4.2 (i) maximisation n minimisation
4.3 (i) important areas
P4- solved problems

P6-CONCEPTS
6.1 Medians, centriod
6.2 Angular bisectors , incentre,excentre
6.3 Altitudes , orthocentre , pedal triangle
6.4 Perpendicular bisectors , circumcentre
6.5 (i) nine points circle
(ii) other properties related to centriod,
circumcentre, orthocentre, centriod
P6 PROBLEMS

P7-C0NCEPTS
7.1 Shifting of origon
7.2 Rotation of axes
P7 PROBLEMS

P8- Pair of St. Line
M – Solved Problem

2 CIRCLE
P1- CONCEPTS
1.1 (a1) Basic definetions n equations of circles –
Standared
(a2) Parametric
(a3) When diametrically end points given
(a4) Appolonious circle

1.2 Point n Circles
P1- SOLVED PROBLEMS

P2 CONCEPTS
2.1 Line as Secant ,Tangent or lies outside circle
2.2 Length of secant , Tangent, Concept of power
of point
2.3 Solving line n circle for common points
2.4 How we get equation of tangent when point lies on circle , point lies outside the circle
2.5 Combined equation of tangent when point lies outside the circle,
2.6 Concept of director circle
P2 SOLVED PROBLEMS

P3-C0NCEPTS
3.1 Chord for which mid point is given n its length
3.2 Concept of chord of contact n its length
3.3 Concept of diametre
P3 SOLVED PROBLEMS

P4 SOLVED CONCEPTS
4.1 Concept of pole n polar
4.2 Intersection of two circlesw n angle between them
4.3 Length of common chords for two circles,its equation
P4 SOLVED PROBLEMS

P5 CONCEPTS
5.1 For two circles common tangents equations
5.2 Lenth of common tangents
P5 SOLVED PROBLEMS

P6 CONCEPTS
6.1 Radical axes n radical centre
6.2 (a1) Family of Circles
(a2) Coaxial System of Circles
6.3 Circumcircle of triangles n quadrilaterals
without evaluating vertices
P6- SOLVED PROBLEMS

PARABOLA
P1 CONCEPTS
1.1 (a1) Definition
(a2) Standard forms of the parabola
(a3) Terms related to parabola
1.2 Parametric Equations of a Parabola
1.3 (a1) Reduction of standard Equation
(a2) General Equation of a Parabola
(a3) Condition when second degree equation Represent parabola
P1 SOLVED PROBLEMS

P2 CONCEPTS
2.1 Position of point with respect to parabola
2.2 (a1) Equation of chord when two points given
(a2) When mid point of chord is given
2.3 Concepts of Diametre
2.4 Length of Chord
P2 SOLVED PROBLEMS

P3 CONCEPTS
3.1 (a1) Condition for Tangency
(a2) Equation of tangent in Different forms
(a3) Point of intersection of tangents
3.2 Equations of chord of contact, Length
3.3 Equations of pair of Tangents
P3 SOLVED PROBLEMS

P4 CONCEPTS
4.1 Equations of Normal in different forms
4.2 Concept of pole n polar
P4 SOLVED PROBLEMS

P5 CONCEPTS
5.1 Special Properties Parabola, Tangents n Normal
5.2 Other Properties of Parabola
P5 SOLVED PROBLEMS
M PROBLEMS

ELLIPSE
P1 CONCEPTS
1.1 (a1) Definition
(a2) Standard forms of the ellipse
(a3) Terms related to ellipse
1.2 Parametric Equations of a ellipse
1.3 (a1) Reduction of standard Equation
(a2) General Equation of a ellipse
(a3) Condition when second degree
Equation Represent Ellipse
P1 SOLVED PROBLEMS

P2 CONCEPTS
1.1 Position of point with respect to ellipse
2.2 (a1) Equation of chord when two points given
(a2) When mid point of chord is given
2.3 Concepts of Diametre
2.4 Length of Chord
P2 SOLVED PROBLEMS

P3 CONCEPTS
3.1 Condition for Tangency, Equation of tangent in
Different forms,Point of intersection of tangents
3.2 Equations of Chord of Contact, Length
3.3 Equations of Pair of Tangents
P3 SOLVED PROBLEMS

P4 CONCEPTS
4.1 Equations of Normal in Different Forms
4.2 Concept of Pole n Polar
P4 SOLVED PROBLEMS

P5 CONCEPTS
5.1 Properties of Tangents n Normal
5.2 Other Properties of Ellipse
5.3 Cunjugate Diametre n Properties
P5 SOLVED PROBLEMS
M PROBLEMS

HYPERBOLA
P1- CONCEPTS
1.1 (a1) Definition
(a2) Standard forms of the Hyperbola
(a3) Terms related to Hyperbola
1.2 Parametric Equations of a hyperbolqa
1.3 (a1)How we get standared equation from foci
Defination
(a2)Condition when second degree equation Represent Hyperbola
P1 SOLVED PROBLEMS

P2 CONCEPTS
1.1 Position of point with respect to hyperbola
2.2 (a1) Equation of chord when two points given
(a2) When mid point of chord is given
2.3 Concepts of diametre
P2 SOLVED PROBLEMS

P3 CONCEPTS
3.1 (a1) Condition for Tangency
(a2) Equation of tangent in Different forms (a3) Point of intersection of tangents
3.2 Equations of chord of contact
3.3 Equations of pair of tangents
P3 SOLVED PROBLEMS

P4 CONCEPTS
4.1 Equations of Normal in Different Forms
4.2 Concept of Pole n Polar
P4 SOLVED PROBLEMS

P5 CONCEPTS
5.1 Properties of Tangents n Normal
5.2 Other Properties of Hyperbolqa
P5 SOLVED PROBLEMS

P6 CONCEPTS
6.1 ASYMPTOTES
6.2 CONJUGATE & RECTANGULAR HYPERBOLA
6.3 HYPERBOLA AND CIRCLE
P6 SOLVED PROBLEMS

To understand this question of pair of lines you must know : The concept of isosceles triangle and how we get equation of lines inclined at given angle with the given line

PROBLEM

To understand this question of pair of lines you must know : How we get angle between two lines whose combined equation is given

To understand this question of PARABOLA you must know : The concept of tangents ,how we get distance of a point lying on parabola from focus

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of tangents ,and double ordinate

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of normal . and condition for which any chord subtend right angle at vertex

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of normal and how we get the length of chord

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of normal and co-normal points

SOLUTION

PROBLEM

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of focal chord and how we get equation of chord when mid point is given

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of normal chord and how we get equation of chord when coordinates of mid point are given

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of latus rectum ,focus , and directrix of parabola

SOLUTION

PROBLEM

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of parametric equations of conics

SOLUTION

PROBLEM

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of common tangents for two parabolas

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of diameter for parabola

SOLUTION

PROBLEM

To understand this question of PARABOLA you must know : The concept of focal chord for parabola and condition of tangent for circle

To understand this question of circles you must know : The concept of family of circles for which point of tangency and equation of tangent is given

PROBLEM

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of diameter and simple equation of circle and basics of quadratic equation

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of family of circles for which point of tangency and equation of tangent is given

SOLUTION

PROBLEM

To understand this question of circles you must know : The condition for which given point lies within triangle and solving simple inequalities

SOLUTION

PROBLEM

To understand this question of circles you must know : The conditions for which two circles intersect at two distinct points

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of common chord for two circles

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of common tangents for two circles

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of pair of tangents drawn from point to the circle

SOLUTION

PROBLEM

To understand this question of circles you must know : The concept of pair of tangents drawn from point to the circle and how we get the intercept of line between two lines