The Circle x2 + y2 – 4x – 4y + 4 = 0 Is Inscribed In A Triangle Which Has Two Of Its Sides Along The Co-ordinate Axes. The Locus Of The Circumcentre Of The Triangle Is x + y – xy + k(x2 + y2)1/2 = 0. Find k.

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The circle x2 + y2 – 4x – 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is x + y – xy + k(x2 + y2)1/2 = 0. Find k.


Correct option is



The given circle is x2 + y2 – 4x – 4y + 4 = 0. This can be re-written as (x– 2)2 + (y – 2)2 = 4 which has centre C (2, 2) and radius 2.

Let the equation of third side is  

Length of perpendicular from (2, 2) on AB = radius = CM


Since origin and (2, 2) lie on the same side of AB



Hence AB is the diameter of the circle passing through ∆OAB, mid point of AB is the centre of the circle i.e., 

Substituting the values of a and b in (1) then


∴ Locus of (hk) is   

                        x + y – xy +   

Hence the required value of k is 1.




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