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Example 14 - Reduce equation root 3x + y - 8 = 0 into normal form

Example 14 - Chapter 10 Class 11 Straight Lines - Part 2
Example 14 - Chapter 10 Class 11 Straight Lines - Part 3

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Example 14 Reduce the equation √3x + y − 8 = 0 into normal form. Find the values of p and ω. √3x + y − 8 = 0 " " √3 "x + y" = 8 Dividing by √((√3)2 + (1)2) = √(3 + 1) = √4 = 2 (√3 𝑥)/2 + 𝑦/2 = 8/2 (√3 𝑥)/2 + 𝑦/2 = 4 𝑥(√3/2) + 𝑦(1/2) = 4 Normal form is x cos 𝜔 + y sin 𝜔 = p Where p is the perpendicular distance from origin & 𝜔 is the angle between perpendicular & the positive x-axis Normal form of any line is x cos 𝜔 + y sin 𝜔 = p Comparing (1) & (2) p = 4 & cos 𝜔 = √3/2 & sin 𝜔 = 1/2 We know that cos 30° = √3/2 and sin 30° = 1/2 Thus, 𝜔 = 30° So, 𝜔 = 30° & p = 4 Thus, the normal form of line is x cos 30° + y sin 30° = 4

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.