If the circle
x squared plus y squared plus 2 g x space plus space 2 f y space plus c space equals space 0 comma space c u t s space e a c h space o f space t h e space c i r c l e s
x squared plus y squared minus 4 space equals space 0 space comma space x squared plus y squared minus 6 x space minus space 8 y space plus 10 space equals space 0 space a n d space x squared plus y squared plus 2 x minus 4 y space minus 2 space equals space 0 space a t space t h e space e x t r e m i t i e s space o f space t h e i r
r e s p e c t i v e space d i a m e t e r s comma space t h e n

a right parenthesis space C space equals space minus 4 space space space space space space space space space B right parenthesis space thin space g plus thin space f space equals space c minus 1 space space space space space space space C right parenthesis space g squared plus f squared minus c space equals space 17 space space space space space space D right parenthesis space space space g. f space equals space minus 6

Asked by Sunil Soni | 10th Aug, 2016, 05:57: PM

Expert Answer:

begin mathsize 16px style E q u a t i o n space o f space t h e space c o m m o n space c h o r d space o f space t h e space c i r c l e space w h o s e space s tan d a r d space e q u a t i o n s space a r e space S subscript 1 equals 0 space a n d space S subscript 2 space equals 0 space i s
S subscript 1 space equals S subscript 2
T h e space r e q u i r e d space c i r c l e space b i s e c t s space e a c h space o f space t h e space g i v e n space c i r c l e s space a t space t h e space e x t r e m e t i e s space o f space t h e space d i a m e t e r space h e n c e space i t space i s space t h e space
c o m m o n space c h o r d space t o space e a c h space o f space t h e space c i r c l e s space g i v e n space t h a t space s h o u l d space p a s s space t h o r u g h 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 s colon
x squared plus y squared minus 4 space equals 0 space h a s space c e n t r e space left parenthesis 0 comma 0 right parenthesis
n o w comma
x squared plus y squared minus 4 space equals space x squared plus y squared plus 2 g x plus 2 f y plus c space....................... b y open parentheses 1 close parentheses
rightwards double arrow space c equals negative 4 space space a s space c e n t r e space i s space open parentheses 0 comma 0 close parentheses

x squared plus y squared space minus 6 x minus 8 y plus 10 equals 0 space h a s space c e n t r e space left parenthesis 3 comma 4 right parenthesis
x squared plus y squared space plus 2 x minus 4 y plus 10 equals 0 space space h a s space c e n t r e space left parenthesis negative 1 comma 2 right parenthesis

S i m i l a r l y space s o l v i n g space f o r space a l l space s e t space o f space e q u a t i o n s space w e space g e t
space space space space space space space space space space c equals negative 4 space space...................................... open parentheses i close parentheses
space space space space space space 6 g plus 8 y plus c equals negative 40............................ open parentheses i i close parentheses
space space space space space minus 2 g plus 4 f plus c equals negative 12........................... open parentheses i i i close parentheses
s o l v i n g space t h e space a b o v e space w e space g e t space c equals negative 4 comma space g equals 6 space a n d space f equals 1
h e n c e space open parentheses a close parentheses space i s space c o r r e c t space end style

Answered by Tripti Agrawal | 12th Aug, 2016, 03:28: PM