Misc 23 - Prove that product of lengths of perpendiculars - Distance of a point from a line

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

Transcript

Misc 23 Prove that the product of the lengths of the perpendiculars drawn from the points (root a^2-b^2,0) and (-root a^2-b^2,0) to the line x/a cos theta +y/b sin theta =1 = b2 Let p1 be the perpendicular distance from point A( ( ^2 ^2 ), 0) to the line / cos + / sin = 1 & p2 be the perpendicular distance from point B( ( ^2 ^2 ), 0) to the line / cos + / sin = 1 We need to show p1 p2 = b2 Calculating p1 & p2 Given line is / cos + / sin = 1 (cos / )x + (sin / )y 1 = 0 = ( ^2 ^2 + ^2 ^2 )/( ^2 ^2 + ^2 ^2 ) ^2 = ( ^2 ^2 + ^2 ^2 )/( ^2 ^2 + ^2 ^2 ) ^2 = ^2 Hence proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.