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

Question

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

Infinity Learn · Accepted Answer

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 $$6x$$−$$8y+7=0$$

$The line L_{1} \equiv 4 x + 3 y - 12 = 0 intersects the x - and y -axis at A and B, respectively. A varıable ine$
$perpendicular to L_{1} intersects the x - and the y -axis at P and Q, respectively. Then the locus of the circumcenter of triangle A B Q is$

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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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$The line L_{1} \equiv 4 x + 3 y - 12 = 0 intersects the x - and y -axis at A and B, respectively. A varıable ine$
$perpendicular to L_{1} intersects the x - and the y -axis at P and Q, respectively. Then the locus of the circumcenter of triangle A B Q is$