Question

If $(0,3)$ and $(0,-3)$ are the limiting points of a coaxial system then the equation of the coaxial system is

• A. $x^2+y^2+2\lambda x+9=0$
• B. $x^2+y^2+2fy+9=0$
• C. $x^2+y^2+2\lambda x-9=0$
• D. $x^2+y^2+2fy-9=0$

Answer 1

The correct option is D $x^2+y^2+2fy-9=0$

Given $(0,3)$ and $(0,3)$ are limiting points of a coaxial system
So, $(0,3),(0,-3)$ and centre of all circle are collinear
So, centre of all circle lies on Y-axis
So, $e{q}^n$ of all circle is
$x^2+y^2+2fy+c=0$
$(0,3)$ satisfy to circle,
So,$9+6f+c=0$ -----(1)
and (0,-3) also satisfy to circle
so, $9-6f+c=0$ --------(2)
$c=-9$
so, $e{q}^n$ of circle is
$\Rightarrow x^2+y^2+2fy-9=0$