# Misc 23 - Chapter 10 Class 11 Straight Lines

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

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 9 years. He provides courses for Maths and Science at Teachoo.