Question

If $(0,0)$ is one limiting point of the coaxial system with radical axis $x+y=1$, then the other limiting point is

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

Answer 1

Answer: (D)

$(1,1)$

The radical axis divides the line segment joining the centre in the ratio of their radii.
Let, $r_1=r_2$
OP is perpendicular to $x+y=1$
So, equation of $OP$ is $y=x$
So, $M=(\frac{1}{2},\frac{1}{2})$
M is a mid-point of limiting point.
So, $P=(1,1)$ is other limiting point.
Hence, option 'D' is correct.