# 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

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.
• 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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