Plane Analytic Geometry - Straight Line

Maths, HSSC-KPK Second Year. This chapter is split into 64 topics and has 1,497 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Perpendicular distance from a point to a line: derivation 20 questions
2. Double-intercept form x/a + y/b = 1 27 questions
3. Reducing the general form to the normal form 22 questions
4. Concurrency of three lines: condition and method 21 questions
5. Perpendicular lines and slopes 25 questions
6. Symmetric (parametric) form of a line 20 questions
7. Second degree homogeneous equation as product of two lines 21 questions
8. Shapes of figures using the distance formula 22 questions
9. Homogeneous equations: definitions and degree 20 questions
10. Slope of a line: definition and derivation 22 questions
11. Angles between lines given by points; inclination 25 questions
12. Equation of the altitude of a triangle 26 questions
13. Concurrent lines of a triangle: centroid, orthocentre, circumcentre 25 questions
14. Nature of the pair of lines: real, coincident or imaginary 20 questions
15. Lines parallel to the coordinate axes 22 questions
16. Joint equation of lines perpendicular to a given pair 21 questions
17. Angle between the lines of a homogeneous pair 20 questions
18. Section formula theory and derivation 20 questions
19. Direction cosines of the normal to a line 20 questions
20. Distance between two points numericals 25 questions
21. Equidistant points and circumcentre 21 questions
22. Unit 6 glossary and key results 22 questions
23. Concurrency numericals: finding k and the common point 24 questions
24. Area of a triangular region: formula and derivation 22 questions
25. Two-point form of a line 24 questions
26. Family of lines through the intersection of two lines 21 questions
27. Intercepts of a line 26 questions
28. Area of a triangle numericals 24 questions
29. Position of a point with respect to a line: theory 22 questions
30. Distance formula derivation and special cases 23 questions
31. Position of a point: numericals 29 questions
32. Normal form of a line: derivation 21 questions
33. Graph of an equation and basic terms 24 questions
34. Angles of a triangle from the slopes of its sides 23 questions
35. Equation of the right (perpendicular) bisector of a segment 26 questions
36. Parallel lines and slopes 24 questions
37. Separating a homogeneous quadratic into two lines 23 questions
38. Angle between two lines given by equations 29 questions
39. Distance from the origin and axis-parallel segments 25 questions
40. Perpendicular and coincident pairs of lines 26 questions
41. Midpoint of a segment 24 questions
42. Angle between lines from their slopes 25 questions
43. Perpendicular distance numericals 26 questions
44. Reducing the general form to standard forms 24 questions
45. Family of lines: origin, equal intercepts and axes conditions 23 questions
46. Finding the ratio of division 25 questions
47. Finding an end point from the midpoint 25 questions
48. Slope from two points numericals 27 questions
49. Point-slope form of a line 22 questions
50. Steepness of lines and reading equations 24 questions
51. Systems of two lines: unique, no or infinitely many solutions 22 questions
52. Area applications: collinearity, unknown vertex, quadrilaterals 22 questions
53. External division of a segment 20 questions
54. General form ax + by + c = 0 and collinearity 22 questions
55. Angle between two lines: derivation and rules 24 questions
56. Slope-intercept form y = mx + c 21 questions
57. Angle bisectors and the incentre 25 questions
58. Centroid and medians of a triangle 27 questions
59. Normal form numericals 23 questions
60. Internal division in a given ratio 30 questions
61. Slope of a line from its equation 26 questions
62. Applications of the point-to-line distance 20 questions
63. Point of intersection of two lines 24 questions
64. Family of lines: parallel, perpendicular and through a point 23 questions