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CBSE Class 12-commerce Answered

please send me the solution
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Asked by spoorthyspoorthy6 | 14 Feb, 2020, 09:02: PM
answered-by-expert Expert Answer
To find the equation of a circle which cuts orthogonally the three circles x2+y2+4x+2y+1=0, 2x2+2y2+8x+6y-3=0 and x2+y2+6x-2y-3=0
L e t space S subscript 1 identical to x squared plus y squared plus 4 x plus 2 y plus 1 equals 0 comma space S subscript 2 identical to x squared plus y squared plus 4 x plus 3 y minus 3 over 2 equals 0 space space a n d space space S subscript 3 identical to x squared plus y squared plus 6 x minus 2 y minus 3 equals 0
T h e space v e r t i c a l space a x i s space o f 1 to the power of s t end exponent space a n d space 2 to the power of n d end exponent space c i r c l e s space i s
S subscript 1 minus S subscript 2 equals 0
rightwards double arrow open parentheses x squared plus y squared plus 4 x plus 2 y plus 1 close parentheses minus open parentheses x squared plus y squared plus 4 x plus 3 y minus 3 over 2 close parentheses equals 0
rightwards double arrow negative y plus 5 over 2 equals 0
rightwards double arrow y equals 5 over 2 space... space left parenthesis i right parenthesis
T h e space v e r t i c a l space a x i s space o f space 2 to the power of n d end exponent space a n d space 3 to the power of r d end exponent space c i r c l e s space i s
S subscript 2 minus S subscript 3 equals 0
rightwards double arrow open parentheses x squared plus y squared plus 4 x plus 3 y minus 3 over 2 close parentheses minus open parentheses x squared plus y squared plus 6 x minus 2 y minus 3 close parentheses equals 0
rightwards double arrow negative 2 x plus 5 y plus 3 over 2 equals 0 space... space left parenthesis i i right parenthesis
F r o m space left parenthesis i right parenthesis
rightwards double arrow negative 2 x plus 25 over 2 plus 3 over 2 equals 0 space space rightwards double arrow space space 2 x equals 14 space space rightwards double arrow space space x equals 7
therefore space C open parentheses 7 comma 5 over 2 close parentheses
rightwards double arrow r equals square root of open parentheses 7 close parentheses squared plus open parentheses 5 over 2 close parentheses squared plus 4 open parentheses 7 close parentheses plus 2 open parentheses 5 over 2 close parentheses plus 1 end root equals square root of 357 over 4 end root equals fraction numerator square root of 357 over denominator 2 end fraction
T h e space e q u a t i o n space o f space c i r c l e space i s space space space open parentheses x minus 7 close parentheses squared plus open parentheses y minus 5 over 2 close parentheses squared equals fraction numerator square root of 357 over denominator 2 end fraction
Answered by Renu Varma | 17 Feb, 2020, 10:50: AM
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