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  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise

Transcript

Example 2 If the angle between two lines is ๐œ‹/4 and slope of one of the lines is 1/2, find the slope of the other line. We know that angle between two lines are tan ฮธ = |(๐‘š2 โˆ’ ๐‘š1)/(1 + ๐‘š1๐‘š2)| Putting ฮธ = ๐œ‹/4 = 180/4 = 45ยฐ Let m1 and m2 be the slope of 2 lines So, m1 = 1/2 We need to find slope of 2nd line i.e. m2 Putting values in formula tan ฮธ = |(๐‘š2 โˆ’ ๐‘š1)/(1 + ๐‘š1๐‘š2)| tan 45ยฐ = |(๐‘š2 โˆ’ 1/2)/(1 + 1/2 ๐‘š2)| 1 = |((2๐‘š_2 โˆ’ 1)/2)/((2 + ๐‘š_2)/2)| 1 = |(2๐‘š2 โˆ’ 1)/(2 + ๐‘š2)| |(2๐‘š2 โˆ’ 1)/(2 + ๐‘š2)|= 1 So, (2๐‘š2 โˆ’ 1)/(2 + ๐‘š2) = 1 & (2๐‘š2 โˆ’ 1)/(2 + ๐‘š2) = โ€“1 Therefore m2 = 3 or m2 = (โˆ’1)/3 . Hence, Slope of the other line is 3 or (โˆ’๐Ÿ)/๐Ÿ‘ (๐Ÿ๐’Ž๐Ÿ โˆ’ ๐Ÿ)/(๐Ÿ + ๐’Ž๐Ÿ) = 1 2m2 โ€“ 1 = (2 + m2) 2m2 โ€“ m2 = 2 + 1 m2 = 3 (๐Ÿ๐’Ž๐Ÿ โˆ’ ๐Ÿ)/(๐Ÿ + ๐’Ž๐Ÿ) = โ€“1 2m2 โ€“ 1 = โ€“(2 + m2) 2m2 โ€“ 1 = โ€“2 โ€“ m2 2m2 + m2 = โ€“2 + 1 3m2 = โ€“1 m2 = (โˆ’1)/3

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.