Question

The equations of two circles are
$x^2+y^2+2\lambda x+5=0$ and $x^2+y^2+2\lambda y+5=0.P$ is any point on the line $x-y=0$. lf $PA$ and $PB$ are the lengths of the tangents from $P$ to the two circles and $PA=3$ then $PB=$______

• A. $1.6$
• B. $6$
• C. $4$
• D. $3$

Answer 1

The correct option is D $3$

$s_1:x^2+y^2+2\lambda x+5=0$

$s_2:x^2+y^2+2\lambda y+5=0$

So, $e{q}^n$ of radial axis of this circles is given by

$s_1-s_2=0$

$\Rightarrow 2\lambda (x-y)=0$

$x=y$

So, length of tangents from any point on line $x-y=0$ are equal.

$\therefore PA=PB$

$PB=PA=3$

$\Rightarrow PB=3$