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CBSE Class 11-science Answered

Prove that part of the tangent at any point of the hyperbola  x^2 /a^2 - y^2/ b^2=1 intercepted between the point of contact and the transverse axis is a harmonic mean between the  lengths of the perpendiculars  drawn from the foci on the normal at the same point.
Asked by sudhanshubhushanroy | 31 Mar, 2018, 02:41: AM
answered-by-expert Expert Answer
begin mathsize 18px style p a r a m e t r i c space f o r m space a t space P
fraction numerator x space s e c space theta over denominator a end fraction minus fraction numerator y space tan theta space over denominator b end fraction equals 1... tan g e n t
fraction numerator a x over denominator space s e c space theta end fraction plus fraction numerator b y over denominator space tan space theta end fraction equals a squared e squared.... n o r m a l
y o u space h a v e space t o space p r o v e
fraction numerator 2 over denominator P Q end fraction equals fraction numerator 1 over denominator N F end fraction plus fraction numerator 1 over denominator T F end fraction
u s e space s i m i l a r i t y space i n space increment G F N space comma increment G Q P comma increment G F T space a n d space d i s tan c e space f o r m u l a end style
Answered by Arun | 02 Apr, 2018, 11:01: AM

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