find the length of the axes,focus,eccentricity,latus rectrum and directrix of the conic represented by 
x^2+2y^2-2x+3y+2=0

Asked by Balbir | 16th Sep, 2016, 05:02: PM

Expert Answer:

straight x squared plus 2 straight y squared minus 2 straight x plus 3 straight y plus 2 equals 0
straight x squared minus 2 straight x plus 1 plus 2 straight y squared plus 3 straight y plus 1 equals 0
open parentheses straight x minus 1 close parentheses squared plus 2 open parentheses straight y squared plus 3 over 2 straight y plus 9 over 16 close parentheses minus 1 over 8 equals 0
open parentheses straight x minus 1 close parentheses squared plus 2 open parentheses straight y plus 3 over 4 close parentheses squared equals 1 over 8
fraction numerator open parentheses straight x minus 1 close parentheses squared over denominator begin display style 1 over 8 end style end fraction plus fraction numerator open parentheses straight y plus 3 over 4 close parentheses squared over denominator begin display style 1 over 16 end style end fraction equals 1
Shifting space of space origin space at space open parentheses 1 comma space minus 3 over 4 close parentheses
Eccentricity space equals space square root of 1 minus fraction numerator begin display style 1 over 16 end style over denominator begin display style 1 over 8 end style end fraction end root equals space square root of 1 minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end root equals fraction numerator 1 over denominator square root of 2 end fraction
Length space of space the space major space axis space equals space 2 cross times fraction numerator 1 over denominator square root of 8 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction
Length space of space the space minor space axis space equals space 2 cross times fraction numerator 1 over denominator square root of 16 end fraction equals 1 half

Length space of space latus space rectum space equals space fraction numerator 2 cross times begin display style 1 over 16 end style over denominator begin display style fraction numerator 1 over denominator square root of 8 end fraction end style end fraction equals fraction numerator 1 over denominator square root of 2 end fraction
Directrix space equals plus-or-minus fraction numerator begin display style fraction numerator 1 over denominator square root of 8 end fraction end style over denominator begin display style fraction numerator 1 over denominator square root of 2 end fraction end style end fraction equals plus-or-minus 1 half


focus space equals open parentheses plus-or-minus fraction numerator 1 over denominator square root of 8 end fraction plus 1 comma negative 3 over 4 close parentheses space straight i. straight e. space open parentheses fraction numerator 1 over denominator square root of 8 end fraction plus 1 comma negative 3 over 4 close parentheses space space and space open parentheses negative fraction numerator 1 over denominator square root of 8 end fraction plus 1 comma negative 3 over 4 close parentheses

Answered by Vijaykumar Wani | 19th Sep, 2016, 06:43: PM