find the equation of a circle which touches both the positive axes and has its center on the line x+2y=3
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Answer:
(x±1)² + ( y ±1 )² = 1 , (x±3)² + ( y ±3 )² = 3²
Step-by-step explanation:
since the circle touches both axes
so let the coordinates of the centre be C ( R , R ) = ( ±R ,± R )
in this case we will get 4 equations
case (i) first quadrant
C = ( R , R )
substitute ( R , R ) in the equation x+2y = 3
R + 2R = 3 , R = 1
(x-1)² + ( y -1 )² = 1
case (ii) 2nd. quadrant
C = ( -R , R )
substitute ( -R , R ) in the equation x+2y = 3
-R + 2R = 3 , R = 3
(x+3)² + ( y -3 )² = 3²
case (iii) 3rd. quadrant
C = ( -R ,- R )
substitute ( R , R ) in the equation x+2y = 3
-R - 2R = 3 , R = -1
(x+1)² + ( y +1 )² = 1
case (i) first quadrant
C = ( R , R )
substitute ( R , -R ) in the equation x+2y = 3
R - 2R = 3 , R = -3
(x+3)² + ( y +3 )² = 3²
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