why in the video lessons the equation x^2+y^2-8x+10y-12=0 is reduced to standard form by adding 16 and 25 on both sides.i want to understand the method applied?
 

Asked by vijayrocks4549 | 13th Oct, 2014, 06:16: AM

Expert Answer:

T h e space e q u a t i o n space o f space t h e space c i r c l e space i n space s tan d a r d space f o r m space i s open parentheses x minus a close parentheses squared plus open parentheses y minus b close parentheses squared equals r squared comma space w h e r e comma space open parentheses a comma b close parentheses space i s space t h e space c e n t r e space o f space t h e space c i r c l e space a n d space r space i s space t h e space r a d i u s space o f space t h e space c i r c l e. T h e space g i v e n space e q u a t i o n space i s space x squared plus y squared minus 8 x plus 10 y minus 12 equals 0 W e space n e e d space t o space c h a n g e space t h e space g i v e n space e q u a t i o n space t o space s tan d a r d space e q u a t i o n space b y space c o n v e r t i n g space t h e space t e r m s space i n space p e r f e c t space s q u a r e space t e r m s. C o n s i d e r space t h e space m i d d l e space t e r m s comma space minus 8 x space a n d space 10 y : T h u s comma space a d d i n g space t h e space h a l f space o f space t h e space m i d d l e space n u m b e r comma space t h a t space i s space open parentheses fraction numerator minus 8 over denominator 2 end fraction close parentheses squared space f o r space x comma space a n d a d d i n g space t h e space h a l f space o f space t h e space m i d d l e space n u m b e r comma space t h a t space i s space open parentheses 10 over 2 close parentheses squared space f o r space y space o n space b o t h space t h e space s i d e s space o f space t h e space e q u a t i o n comma space w e space h a v e comma x squared plus y squared minus 8 x plus 10 y minus 12 plus 16 plus 25 equals 16 plus 25 rightwards double arrow x squared minus 8 x plus 16 plus y squared plus 10 y plus 25 equals 16 plus 25 plus 12 rightwards double arrow open parentheses x squared minus 8 x plus 16 close parentheses plus open parentheses y squared plus 10 y plus 25 close parentheses equals 53 rightwards double arrow open parentheses x minus 4 close parentheses squared plus open parentheses y plus 5 close parentheses squared equals 53 rightwards double arrow open parentheses x minus 4 close parentheses squared plus open parentheses y plus 5 close parentheses squared equals open parentheses square root of 53 close parentheses squared T h u s comma space t h e space s tan d a r d space e q u a t i o n space o f space t h e space c i r c l e space i s comma open parentheses x minus 4 close parentheses squared plus open parentheses y plus 5 close parentheses squared equals open parentheses square root of 53 close parentheses squared comma space w h e r e space left parenthesis 4 comma minus 5 right parenthesis space i s space t h e space c n t r e space o f space t h e space c i r c l e space a n d space square root of 53 space i s space t h e space r a d i u s space o f space t h e space c i r c l e.

Answered by Vimala Ramamurthy | 13th Oct, 2014, 10:02: AM