question_answer

The line \[{{L}_{1}}:4x+3y-12=0\]intersects the x-and y-axis at A and B, respectively. A variable line perpendicular to \[{{L}_{1}}\] intersects the x- and the y. the circumventer of triangle ABQ is

A) \[3x-4y+2=0\]

B) \[4x+3y+7=0\]

C) \[6x-8y+7=0\]

D) None of these

Correct Answer: C

Solution :

[c] Clearly, the circumventer of triangle ABQ will lie on the perpendicular bisector of line AB, Now, the equation of perpendicular bisector of line AB is \[3x-4y+7/2=0.\] Hence, the locus of circumventer is \[6x-8y+7=0.\]