The circle is inscribed in a triangle which has two of its sides along the coordinate axes.The locus of the circumcentre of the triangle is
The value of is?
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The equation of L is x / a + y / b = 1 and the distance of centre to the line is 1 / a 2 + 1 / b 2 ∣ 2 / a + 2 / b − 1 ∣ = 2 .Now circumcentre is the point (a/2,b/2) since it bisects line L between the axes (since it forms a right angle triangle).Slightly manipulating the equation we get ( a / 2 ) 2 + ( b / 2 ) 2 a / 2 + b / 2 − ( a / 2 ) ( b / 2 ) = − 1 Which matches with the equation in question.Hence k=1.Replace a/2 with x and b/2 with y to get that equation.