Misc 3 - Lines which cut-off intercepts on axes whose sum - Miscellaneous

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

Transcript

Misc 3 Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and โ€“6, respectively. Equation of a line by intercept form is ๐‘ฅ/๐‘Ž + ๐‘ฆ/๐‘ = 1 where a is x โ€“ intercept & b is y โ€“ intercept Given that sum of intercept is 1 i.e. a + b = 1 Product of intercept is โˆ’ 6 i.e. a ร— b = โˆ’ 6 From (1) a + b = 1 a = 1 โ€“ b Putting value of a in (2) a ร— b = โˆ’ 6 (1 โ€“ b) ร— b = โˆ’ 6 b โ€“ b2 = โˆ’ 6 0 = b2 โ€“ b โ€“ 6 b2 โ€“ b โ€“ 6 = 0 b2 โ€“ 3b + 2b โ€“ 6 = 0 b(b โ€“ 3) + 2(b โ€“ 3) = 0 (b โ€“ 3) (b + 2) = 0 So, b = 3, & b = โ€“ 2 Hence a = โˆ’ 2, b = 3 & a = 3, b = โˆ’ 2 Now, finding equation of lines Hence, equation of lines are โˆ’ 2x + 3y + 6 = 0 & 3x โˆ’ 2y + 6 = 0

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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.