Question

Find the equation of the circle which touches the axes and whose centre lies on x-2y=3.

Answer 1

touching axes means that both the coordinates of the centre will be in the form (a,a) hence we can say the eqn will be (x-a)^2 +(y-a)^2 = a^2 and since the centre lied on the line x-2y=3 the coordinates (a,a) will satisfy it, a-2a=3, hence a becomes -3 how put the values of a in the given eqn of circle that will be the answer

Answer 2

let the centre be ( h,k) 
as cicle touches both axes so 
h= k 
center lies on line x- 2y = 3
so h-2h = 3
or h = -3 = k
so centre is ( - 3, - 3 )
radius = h=k= -3
so equation of reuired circle is --------
( x+ 3)^2 + ( y+3)^2 = (-3)^2
or x^2 + y^2 + 6x + 6y + 9 =0 ans
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