Question

find the equation of a circle which touches both the positive axes and has its center on the line x+2y=3​

Answer 1

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