The line L1≡4x+3y−12=0 intersects the x− and y -axis at A and B, respectively. A varıable ine  perpendicular to L1 intersects the x - and the y -axis at P and Q , respectively. Then the locus of the circumcenter  of triangle ABQ is

Clearly, the circumcenter of triangle ABQ will lie on the perpendicular bisector of line AB.If A(3,0) and B(0,4) then midpoint of AB =32,2 Let the equation of perpendicular bisector be 3x-4y+k=0, which passes through 32,2Now, the equation of perpendicular bisector of line AB is 3x−4y+72=0 . Hence,  the locus of circumcenter is 6x−8y+7=0