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

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

Transcript

Misc 2 Find the values of and p, if the equation is the normal form of the line 3x + y + 2 = 0 . 3x + y + 2 = 0 2 = 3x y 3x y = 2 Dividing by (( 3)2 + ( 1)2) = (3 + 1) = 4 = 2 both sides ( 3 )/2 /2 = 2/2 ( 3 )/2 /2 = 1 (( 3)/2) + (( 1)/2)y = 1 Normal form of any line is x cos + y sin = p Comparing (1) & (2) p = 1 & cos = ( 3)/2 & sin = ( 1)/2 Now, finding = 180 + 30 = 210 So, the normal form of line is x cos 210 + y sin 210 = 2 Hence, angle = 210 = 210 /(180 ) = 7 /6 & perpendicular distance = p = 2

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