Chapter 4 (Introduction to Analytic Geometry) FSc Part 2 Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 5
Type: Notes

TITLESOLUTION
Exercise 4.1View
Exercise 4.2 View
Exercise 4.3 View
Exercise 4.4 View
Exercise 4.5 View

In this chapter we will read these topics:

  • What are the meanings of the word geometry?
  • Who was the founder of geometry.
  • What is Plane geometry.
  • What is Solid geometry.
  • What is analytic geometry?
  • Define a coordinate plane and coordinate axes.
  • Define abscissa and ordinate of a point.
  • Define quadrants.
  • State and prove distance formula.
  • Distance of point P(x,y) from x-axis is |y| and from y-axis is |x|.
  • Distance measured non-parallel to coordinate axes is called undirected distance.
  • Distance measured parallel to the coordinate axes is called directed distance.
  • State and prove the Ration formula or Division formula.
  • State and prove the Ration formula/Division formula for external division.
  • Derive mid-point formula from ratio formula.
  • Define Median of a triangle.
  • What do you mean by concurrent lines.
  • Define Centroid of a triangle.
  • Show that medians of a triangle are concurrent.
  • What are coordinates of centroid of a triangle.
  • Define angle bisector and in-center of a triangle.
  • Define the translation of axes.
  • Write the equations of translation of axes.
  • Define the rotation of axes.
  • Write the equation of axes.
  • Write the equation of rotation of axes.
  • Define the inclination of a line.
  • Define the slope or gradient of a line.
  • Write formula for slope of a line passing through two points.
  • What is the condition of two parallel lines.
  • What is the condition of two perpendicular lines.
  • When three points are said to be colinear.
  • What is the equation of line parallel to x-axis.
  • What is the equation of line parallel to y-axis.
  • What do you mean by intercepts.
  • State and prove the equation of line in slop-intercept form.
  • Types of lines.
  • State and prove equation of line in point-slope form.
  • Derive the symmetric form of a line.
  • State and prove equation of line in two-points form.
  • Equation of non-vertical straight line passing through two points.
  • State and prove equation of line in intercept form.
  • State and prove equation of line in normal form.
  • Describe the position of a point with respect to line.
  • Point of intersection and condition of concurrent.
  • Prove that altitudes of a triangle are concurrent.
  • Prove that the right bisector of triangle are concurrent.
  • Angle between two lines.
  • Two lines l1 and l2 are parallel if and only if m1=m2.
  • Find point of intersection of the lines.
  • Find equation of line.
  • Find acute angle.
  • Find interior angles of triangles.
  • Find interior angle of the quadrilateral.
  • Find the center of the circumcircle of the triangle.
  • Define the homogeneous equation of degree n in x and y variables.
  • Define general homogeneous equation of second degree in x and y variables.
  • Find a joint equation of the lines through the origin and perpendicular to the lines.
  • Find the area of the bounded region.
  • Area of tapezium

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