Question

If a circle passes through the points where the lines $3kx-2y-1=0$ and $4x-3y+2=0$ meet the coordinate axes then $k=$

• A. $1$
• B. $-1$
• C. $\frac{1}{2}$
• D. $\frac{-1}{2}$

Answer 1

Answer: (C)

The line $3kx-2y-1=0$ meets $x$-axis and $y$-axis at $A\left(\frac{1}{3k},0\right)$ and $B\left(0,-\frac{1}{2}\right)$, respectively.
Also, the line $4x-3y+2=0$ cuts $x$-axis and $y$-axis at $C\left(-\frac{1}{2},0\right)$ and $D\left(0,\frac{2}{3}\right)$, respectively.

Since the four points are concyclic, we have
$OB\times OD=OA\times OC$
$\Rightarrow (1/2)(2/3)=(1/3k)(1/2)$
$\Rightarrow k=1/2$