Question

equations of a circle touching lines x=-1,x=3 and y=3

Answer 1

Answer:

let eq. be

(x-a)² + (y-b)² = r²

substituting 3 values of x,y [ (-1,0), (3,0), (0,3) ]

1. (-1-a)² = r²

   r = -(1+a) or (1+a)

2.  (3-a)² = r²

    r = 3-a or a-3

from 1 & 2 above

r = 3-a = 1+a is the possible solution since r is a positive value, hence,

2a = 2 => a=1 and r = 2

3.  (3-b)² = r²

  => (3-b)² = 4

  => 3-b = 2 or -2

  => b = 1 or 5

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Hence Equations of Circle ->

1. ⇒  (x-1)² + (y-1)² = 4  

2. ⇒  (x-1)² + (y-5)² = 4  and