Misc 2 - Find values of theta, p, if equation is normal form - Miscellaneous

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Misc 2 Find the values of ๐œƒ and p, if the equation is the normal form of the line โˆš3x + y + 2 = 0 . โˆš3x + y + 2 = 0 2 = โ€“ โˆš3x โ€“ y โ€“ โˆš3x โ€“ y = 2 Dividing by โˆš((โˆ’โˆš3)2 + (โˆ’1)2) = โˆš(3 + 1) = โˆš4 = 2 both sides (โˆ’โˆš3 ๐‘ฅ)/2 โˆ’ ๐‘ฆ/2 = 2/2 (โˆ’โˆš3 ๐‘ฅ)/2 โˆ’ ๐‘ฆ/2 = 1 ((โˆ’โˆš3)/2)๐‘ฅ + ((โˆ’1)/2)y = 1 Normal form of any line is x cos ๐œ” + y sin ๐œ” = p Comparing (1) & (2) p = 1 & cos ฯ‰ = (โˆ’โˆš3)/2 & sin ฯ‰ = (โˆ’1)/2 Now, finding ฯ‰ โˆด ฯ‰ = 180ยฐ + 30ยฐ = 210ยฐ So, the normal form of line is x cos 210ยฐ + y sin 210ยฐ = 2 Hence, angle = 210ยฐ = 210 ร— ๐œ‹/(180ยฐ ) = 7๐œ‹/6 & perpendicular distance = p = 2

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