Question

If $x=1$ is the equation of the common radical axis and $(2,3)$ is one limiting point of a coaxial system, then the other limiting point is

• A. $(3,0)$
• B. $(0,3)$
• C. $(0,1)$
• D. $(0,-3)$

Answer 1

The correct option is B $(0,3)$

$x=1$ is the equation of the common radical axis

So, all centre of the circle lie on the line perpendicular to $x=1$ and passing through $(2,3)$
So, the line in which all centres lie is $y=3$
and $P$ is the mid-point of limiting points.
$[r_1=r_2]$
So, other limiting point is
$x=2\times 1-2=0$
and $y=2\times 3-3=3$
$(0,3)$ is the other limiting point.