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If p , p’ are the lengths of the perpendiculars from the origin from the straight line, whose equations are xsecR+ycosecR=a amd xcosR-ysinR=acos2R, then show that 4p2 + 4p’2=a2 .

If p , p’ are the lengths of the perpendiculars from the origin from the straight line, whose equations are xsecR+ycosecR=a amd xcosR-ysinR=acos2R, then show that 4p2 + 4p’2=a2 .

Grade:11

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student
from what i understand by your representation.
\\p'= { acos^2R \over \sqrt{sin^2R+cos^2R}}=|acos^2R| \\p=|{ a \over \sqrt{sec^2R+cosec^2R} }|=|{ asinRcosR }|=|{asin2R \over 2}| \\=>4p^2 + 4p'^2 \\=>4(a^2cos^4R+{a^2sin^22R \over 4}) \\=>cos^2R={1 +cos2R \over 2} \\=>4a^2( { 1/4+1/4+cos2R/2})=4a^2(1+cos2R)/2= \\=>4a^2cos^2R
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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