1 A 1 B 1 C 1 D 2 3 4 5 6

RD Sharma - Mathematics

23. The Straight Lines

1. Sets
2. Relations
3. Functions
4. Measurement of Angles
5. Trigonometric Functions
6. Graphs of Trigonometric Functions
7. Values of Trigonometric Functions at Sum of Difference of Angles
8. Transformation Formulae
9. Values of Trigonometric Functions at Multiples and Submultiple of an Angles
10. Sine and Cosine Formulae and their Applications
11. Trigonometric Equations
12. Mathematical Induction
13. Complex Numbers
14. Quadratic Equations
15. Linear Inequations
16. Permutations
17. Combinations
18. Binomial Theorem
19. Arithmetic Progressions
20. Geometric Progressions
21. Some Special Series
22. Brief Review of Cartesian System of Rectangular Co-ordinates
23. The Straight Lines
24. The Circle
25. Parabola
26. Ellipse
27. Hyperbola
28. Introduction to 3-D Coordinate Geometry
29. Limits
30. Derivatives
31. Mathematical Reasoning
32. Statistics
33. Probability

Exercise 23.1

1 A 1 B 1 C 1 D 2 A 2 B 2 C 3 A 3 B 3 C 3 D 4 5 A 5 B 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Exercise 23.2

Exercise 23.3

1 2 3 4 5 6 7 8

Exercise 23.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.5

1 A 1 B 1 C 1 D 1 E 1 F 2 A 2 B 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.6

1 A 1 B 2 3 A 3 B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Exercise 23.7

1 A 1 B 1 C 1 D 2 3 4 5 6 7 8 9 10

Exercise 23.8

1 2 3 4 5 6 7 8 9 10 11 12 13

Exercise 23.9

1 2 A 2 B 2 C 2 D 2 E 3 4 5 6 7 8

Exercise 23.10

1 A 1 B 1 C 2 A 2 B 3 A 3 B 3 C 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Exercise 23.11

1 A 1 B 1 C 2 3 4 5 6 7 8

Exercise 23.12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Exercise 23.13

1 A 1 B 1 C 1 D 1 E 2 3 4 5 6 7 8 9 10

Exercise 23.14

Exercise 23.15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.16

1 A 1 B 1 C 1 D 2 3 4 5 6

Exercise 23.17

Exercise 23.18

1 2 3 4 5 6 7 8 9 10 11 12 13

Exercise 23.19

1 2 3 4 5 6 7 8 9 10 11

Very Short Answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

MCQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Q. 63.9( 7 Votes )

Find the ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0

Class 11th RD Sharma - Mathematics 23. The Straight Lines

Answer :

Given:

Lines A: 3x + 4y + 5 = 0 and B: 3x + 4y – 5 = 0

And also C: 3x + 4y + 2 = 0

To find:

Ratio in which line C divides the distance between the lines A and B

Explanation:

The distance between two parallel line ax + by + c1 = 0 and ax + by + c2 = 0 is

Therefore the distance between two parallel line 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is

The distance between the line 3x + 4y + 2 = 0 and 3x + 4y – 5 = 0 is

Hence, the required ratio

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PREVIOUSFind the equation of the line mid-way between the parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.NEXTProve that the area of the parallelogram formed by the linesa1x + b1y + c1 = 0, a1x + b1y + d1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is sq. units.Deduce the condition for these lines to form a rhombus.

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