The circle x2 + y2 - 4x - 4y + 4 = 0 is inscribed in a triangle, which has two of its sides along the coordinate axes. If the locus of the circumcentre is of the form
x + y - xy + k(x2 + y2)1/2= 0. Find k.
The Attempt at a Solution
The centre of the given circle is (2,2) and its radius is 2 units. Let the circumcentre be (h,k).
The intercepts of one side of the triangle on x and y axes are 2h and 2k respectively.
The distance between incentre and circumcentre is (R2 - 2Rr)1/2, where R = (h2 + k2)1/2
Square of it must be equal to (h -2)2 + (k -2)2
i.e. (R2 - 2Rr) = (h -2)2 + (k -2)2
On solving I got
h + k - (h2 + k2)1/2 = 2
which is not of the form given.
Please point out my mistake if any.