F i n d 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 w i t h space c e n t r e space left parenthesis 1 comma 1 right parenthesis space a n d space t o u c h e s space t h e space l i n e space 2 x plus 3 y equals negative 5

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Asked by Topperlearning User | 15th Nov, 2016, 09:59: PM

Expert Answer:

T h e space l i n e space 2 x plus 3 y plus 5 equals 0 space t o u c h e s space t h e space c i r c l e space s o space t h i s space l i n e space i s space a space tan g e n t space t o space t h e space c i r c l e.
T h e space p e r p e n d i c u l a r space d i s tan c e space f r o m space t h e space c e n t r e space t o space t h e space tan g e n t space l i n e space w i l l space g i v e space t h e space r a d i u s space s o
R a d i u s equals open vertical bar fraction numerator 2.1 plus 3.1 plus 5 over denominator square root of 2 squared plus 3 squared end root end fraction close vertical bar equals fraction numerator 10 over denominator square root of 13 end fraction
S o space 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 1 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 100 over 13
rightwards double arrow 13 x squared plus 13 y squared minus 26 x minus 26 y minus 74 equals 0

Answered by  | 15th Nov, 2016, 11:59: PM