Ch 4 Maths Class 12 Solutions

• Important ch 4 maths class 12 important questions for Intermediate part-II students. 
• Geometry:- The geometry is derived from two Greek words Geo (Earth) and Metron (Measurement). It means knowledge of measurement of earth. Geometry is branch of mathematics that deals the shape and size of things.
• Analytic geometry:- An analytic geometry or coordinates geometry, Points could be represented by numbers, lines and curves represented by equations. A French philosopher and mathematician Rene Descartes (1596-1650A.D.) introduced algebraic methods in geometry named as analytical geometry (or coordinate geometry).
• Definition of two-dimensional rectangular or Cartesian coordinate system.
• What is the Distance formula and understanding by Graph and with examples?
• Important ch 4 maths class 12 for Intermediate part-II students.
• Point dividing the join of two points in a given ratio.
• Complete Solutions of Exercise 4.1,4.2,4.3,4.4 of Chapter number 4 Introduction to Analytic Geometry.
• What is the Translation and rotation of the Axis?
• Important ch 4 maths class 12 for Intermediate part-II students.
• What are the equations of straight lines?
• Slope or Gradient of a separate line in joining two points.
• Equation of a straight line parallel to the y-axis or perpendicular to the x-axis.
• Derivation of a standard form of equations of straight lines.
• Important class 12 maths 4.1 for Intermediate part-II students.
• Point slope form of equations of a straight line.
• Symmetric form of equations of a straight line.
• A linear equation in two variables represents a separate line.
• To transform the general linear equation to standard forms.
• Important class 12 maths ch 4 for Intermediate part-II students.
• Position of a point with respect to a line.
• Two and Three straight lines.
• The point of intersection of two straight lines.
• Important class 12 maths ch 4 ex 4.1 for Intermediate part-II students.
• Condition of concurrency of three straight lines.
• The equation of lines through the point of intersection of two lines.
• Important class 12 maths ch 4 ex 4.2 for Intermediate part-II students.
• Distance of a point from a line and Distance between two parallel lines.
• (i) Two geometric figures are similar if one is enlargement of other.
• (ii) In two triangles, if two corresponding angles are congruent, then triangles are similar.
• (iii) If the directed distances AP and PB have the same sign, then their ratio is positive and Pis said to divide AB internally.
• (iv) If the directed distances AP and PB have opposite signs i-e., P is beyond AB, then their ratio is negative and P is said to divide AB externally. Thus P is said to divide the line segment AB in ratio K₁: K₂ internally or externally according as Plies b/w AB or beyond AB.
• (v) If K₁: K₂=1:1, then P becomes midpoint of AB and coordinates of P are: x = x_1 + x_2/2,  y= y_1 + y_2/2
• (vi) The above theorem is valid in whichever quadrant A and B lie.
• Important class 12 maths ch 4 ex 4.3 for Intermediate part-II students.
• Find the Area of a triangular region whose vertices are given.
• Important maths class 12 chapter 4 exercise 4.1 for Intermediate part-II students.
• The angle between two lines and the Equation of a straight line in a matrix form.
• To find the measure of the angle between the lines represented by ax2 + 2hxy+ by2=0.
• Important exercise 4.1 class 12 for Intermediate part-II students.
• Important exercise 4.2 class 12 for Intermediate part-II students.
• Important exercise 4.3 class 12 for Intermediate part-II students.
• Important exercise 4.4 class 12 for Intermediate part-II students.