NCERT solution Class 11 straight lines

NCERT Solutions

Class 11 Maths

Straight Lines

NCERT Questions

Ex.10.1 Q.1
Ex.10.1 Q.2
Ex10.1 Q3
Ex10.1 Q.4
Ex10.1 Q.5
Ex.10.1 Q.6
Ex10.1 Q.7
Ex10.1 Q.8
Ex.10.1 Q.9
Ex.10.1 Q.10
Ex.10.1 Q.11
Ex.10.1 Q.12
Ex.10.1 Q.13
Ex10.1 Q.14
Ex.10.2 Q.1
Ex.10.2 Q.2
Ex.10.2 Q.3
Ex10.2 Q.4
Ex10.2 Q.5
Ex.10.2 Q.6
Ex.10.2 Q.7
Ex10.2 Q.8
Ex.10.2 Q.9
Ex.10.2 Q.10
Ex.10.2 Q.11
Ex.10.2 Q.12
Ex.10.2 Q.13
Ex.10.2 Q.14
Ex.10.2 Q.15
Ex.101.2 Q.16
Ex.10.2 Q.17
Ex.10.2 Q.18
Ex.10.2 Q.19
Ex.10.2 Q.20
Ex.10.3 Q.1
Ex.10.3 Q.2
Ex.10.3 Q.3
Ex.10.3 Q.4
Ex.10.3 Q.5
Ex.10.3 Q.6
Ex.10.3 Q.7
Ex.10.3 Q.8
Ex.10.3 Q.9
Ex.10.3 Q.10
Ex.10.3 Q.11
Ex.10.3 Q.12
Ex.10.3 Q.13
Ex.10.3 Q.14
Ex.10.3 Q.15
Ex.10.3 Q.16
Ex.10.3 Q.17
Ex.10.3 Q.18
Ex.Misc. Q.1
Ex.Misc. Q.2
Ex.Misc. Q.3
Ex.Misc. Q.4
Ex.Misc. Q.5
Ex.Misc.Q.6
Ex.Misc. Q.7
Ex.Misc. Q.8
Ex.Misc. Q.9
Ex.Misc. Q.10
Ex.Misc. Q.11
Ex.Misc. Q.12
Ex.Misc. Q.13
Ex.Misc. Q.14
Ex.Misc. Q.15
Ex.Misc.Q.16
Ex.Misc. Q18
Ex.Misc. Q.19
Ex.Misc.Q.20
Ex.Misc.Q.21
Ex.Misc.Q.22
Ex.Misc. Q.23
Ex.Misc. Q.24

Ex.Misc. Q.23

Prove that the product of the lengths of the perpendiculars drawn from the points

{√ (a² - b²), 0} and {-√ (a² - b²), 0} to the line + = 1 is b².

The equation of the given line is

+ = 1

=> bx cos θ + ay sin θ – ab = 0 ……………. (1)

Length of the perpendicular from the point {√ (a² - b²), 0} to the line 1 is

p₁ = |b cos θ × √ (a² - b²) + a sin θ × 0 - ab| ÷ √ (b² cos² θ + a² sin² θ)

= |b cos θ × √ (a² - b²) - ab| ÷ √ (b² cos² θ + a² sin² θ) ……. (2)

Length of the perpendicular from the point {-√ (a² - b²), 0} to the line 1 is

p₂ = |b cos θ × {-√ (a² + b²)} + a sin θ × 0 - ab| ÷ √ (b² cos² θ + a² sin² θ)

= |b cos θ × √ (a² + b²) + ab| ÷ √ (b² cos² θ + a² sin² θ) ………. (3)

Multiply equation (2) and (3), we get

p₁p₂ = {|b cos θ × √ (a² - b²) - ab|× |b cos θ × √ (a² + b²) + ab|} ÷ {√ (b² cos² θ + a² sin² θ)}²

= {|b cos θ × √ (a² - b²) - ab|× |b cos θ × √ (a² + b²) + ab|} ÷ (b² cos² θ + a² sin² θ)

= {|b cos θ × √ (a² - b²)}² – (ab)²| ÷ (b² cos² θ + a² sin² θ)

= |b² cos² θ × (a² - b²) – a² b²| ÷ (b² cos² θ + a² sin² θ)

= |a²b² cos² θ – b⁴ cos² θ – a² b²| ÷ (b² cos² θ + a² sin² θ)

= b²|a²cos² θ – b² cos² θ – a²| ÷ (b² cos² θ + a² sin² θ)

= b²|a²cos² θ – b² cos² θ – a² sin² θ - a² cos² θ| ÷ (b² cos² θ + a² sin² θ)

= b²|-(b² cos² θ + a² sin² θ) | ÷ (b² cos² θ + a² sin² θ)

= b²(b² cos² θ + a² sin² θ) ÷ (b² cos² θ + a² sin² θ)

= b²

Hence, p₁p₂ = b²

Straight Lines Class 11 Maths NCERT Chapter 9 NCERT Solutions

Solving NCERT textbook questions of Straight Lines Class 11 Maths NCERT Chapter 9 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 11 Maths Straight Lines, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 11 Maths Straight Lines Online Test on LearnoHub.com.
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By following these steps and actively engaging with the NCERT solutions module of Class 11 Maths Straight Lines NCERT Chapter 9, you can improve your learning outcomes, develop a better grasp of the subject, and perform well in exams and other academic assessments. Remember that consistent practice, understanding, and application of knowledge are key to academic success.

NCERT solutions of Straight Lines Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Straight Lines NCERT solutions.