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Ex 10.3, 3 - Reduce equations into normal form - Class 11 - Ex 10.3

Ex 10.3, 3 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.3, 3 - Chapter 10 Class 11 Straight Lines - Part 3

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Ex10.3, 3 Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. x 3 y + 8 = 0 x 3 y + 8 = 0 8 = x + 3 x + 3 = 8 Divide equation by (( 1)2 + ( 3)^2 ) = (1 + 3)= 4 = 2 ( + 3 )/2 = 8/2 ( )/2 + 3/2y = 4 x(( 1)/2) + y ( 3/2) = 4 Normal form of any line is x cos + y sin = p Comparing (1) & (2) p = 4 & cos = 1/2 & sin = 3/2 Now, finding = 180 60 = 120 So, the normal form of line is x cos 120 + y sin 120 = 4 Hence perpendicular distance from origin = p = 4 & angle between perpendicular & the + ve x-axis = = 120

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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.