Question

The limiting points of the coaxial system
$x^2+y^2+2fy+9=0$ ( $f$ is a variable) are

• A. $(\pm 3,0)$
• B. $(\pm 9,0)$
• C. $(0,\pm 9)$
• D. $(0,\pm 3)$

Answer 1

The correct option is D $(0,\pm 3)$

Ror limiting points,
$r=\sqrt{f^2-9}=0$
$\Rightarrow f=\pm 3$
And radical axis of given system is $y=0$
Limiting points lie on Y-axis i.e. $(x=0)$
So, limiting point is $(0,f)\Rightarrow (0,\pm 3)$.