If space p space i s space t h e space l e n g t h space o f space p e r p e n d i c u l a r space d r a w n space f r o m space o r i g i n space t o space l i n e space x over a plus y over b space equals space 1 space a n d space
a squared comma p squared comma b squared space a r e space i n space A. P. space comma space t h e n space p r o v e space t h a t space a to the power of 4 plus b to the power of 4 space equals space 0 space.

Asked by manish.kkd4 | 20th Feb, 2019, 12:20: PM

Expert Answer:

begin mathsize 16px style straight x over straight a plus straight y over straight b equals 1
Perpendicular space distance space from space the space origin space to space the space line
straight p equals fraction numerator negative 1 over denominator square root of begin display style 1 over straight a squared plus 1 over straight b squared end style end root end fraction
straight p squared equals fraction numerator 1 over denominator 1 over straight a squared plus 1 over straight b squared end fraction
fraction numerator begin display style 1 end style over denominator begin display style straight a squared end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight b squared end style end fraction equals 1 over straight p squared space space space.... left parenthesis straight i right parenthesis
As space straight a squared comma straight p squared space and space straight b squared space are space in space straight A. space straight P.
2 straight p squared equals straight a squared plus straight b squared
straight p squared equals fraction numerator straight a squared plus straight b squared over denominator 2 end fraction space space.... left parenthesis ii right parenthesis
Substitute space in space left parenthesis straight i right parenthesis space
1 over straight a squared plus 1 over straight b squared equals fraction numerator 1 over denominator fraction numerator straight a squared plus straight b squared over denominator 2 end fraction end fraction
fraction numerator straight a squared plus straight b squared over denominator straight a squared straight b squared end fraction equals fraction numerator 2 over denominator straight a squared plus straight b squared end fraction
open parentheses straight a squared plus straight b squared close parentheses squared equals 2 straight a squared straight b squared
straight a to the power of 4 plus 2 straight a squared straight b squared plus straight b to the power of 4 equals 2 straight a squared straight b squared
straight a to the power of 4 plus straight b to the power of 4 equals 0 end style

Answered by Sneha shidid | 20th Feb, 2019, 01:01: PM