CBSE Class 11-science Answered

Find the equation of the circle which passes through the points (2,-2), and (3, 4) and whose centre lies on the line x + y = 2.

Asked by Topperlearning User | 20 Oct, 2016, 05:33: AM

Expert Answer

$L e t space 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 b e space left parenthesis x minus h right parenthesis squared plus left parenthesis y minus k right parenthesis squared equals r squared w h e r e space left parenthesis h comma k right parenthesis space i s space t h e space c e n t r e space a n d space r equals space r a d i u s G i v e n space c i r c l e space p a s s e s space t h r o u g h space left parenthesis 2 comma negative 2 right parenthesis space a n d space left parenthesis 3 comma 4 right parenthesis space s o space w e space h a v e left parenthesis 2 minus h right parenthesis squared plus left parenthesis negative 2 minus k right parenthesis squared equals r squared rightwards arrow circle enclose 1 left parenthesis 3 minus h right parenthesis squared plus left parenthesis 4 minus k right parenthesis squared equals r squared rightwards arrow circle enclose 2 circle enclose 1 equals circle enclose 2 h squared plus 4 minus 4 h plus k squared plus 4 plus 4 k equals h squared plus 9 minus 6 h plus k squared plus 16 minus 8 k 2 h plus 12 k equals 17 rightwards arrow circle enclose 3 G i v e n space left parenthesis h comma k right parenthesis space l i e s space o n space x plus y equals 2 space s o h plus k equals 2 rightwards arrow circle enclose 4 s o l v i n g space circle enclose 4 space a n d space circle enclose 3 space w e space g e t space h equals 7 over 10 space k equals 13 over 10 space t h e space r a d i u s space r space i s space t h e space d i s tan c e space b e t w e e n space left parenthesis h comma k right parenthesis space a n d space left parenthesis 3 comma 4 right parenthesis s o space r squared equals left parenthesis 7 over 10 minus 3 right parenthesis squared plus left parenthesis 13 over 10 minus 4 right parenthesis squared equals 1258 over 100 T h e space r e q u i r e d space e q u a t i o n space i s left parenthesis x minus 7 over 10 right parenthesis squared plus left parenthesis y minus 13 over 10 right parenthesis squared equals space 1258 over 100 left parenthesis 10 x minus 7 right parenthesis squared plus left parenthesis 10 y minus 13 right parenthesis squared equals 1258$