Question

Consider a variable line $L$ which passes through the point of intersection ' $P$ ' of the lines $3x+4y-12=0$ and $x+2y-5=0$, meeting the coordinate axes at the points $A$ and $B$.
Locus of the feet of the perpendicular from the origin on the variable line ' $L$ ' has the equation

• A. $2\left(x^2+y^2\right)-3x-4y=0$
• B. $2\left(x^2+y^2\right)-4x-3y=0$
• C. $x^2+y^2-2x-y=0$
• D. $x^2+y^2-x-2y=0$

Answer 1

Answer: (B)

Point of intersection of the line
$3x+4y-12=0$
$x+2y-5=0$
is $x=2$ and $y=3/2$

$\frac{k}{h}\cdot \frac{k-(3/2)}{h-2}=-1$
$\frac{k}{h}\cdot \frac{2k-3}{h-2}=-2$
$2h(h-2)+k(2k-3)=0$
$2\left(x^2+y^2\right)-4x-3y=0$