Question

Minimum radius of cirlce which is orthogonal with both the circles $x^2+y^2-12x+35=0$ and $x^2+y^2+4x+3=0$ is

• A. $4$
• B. $3$
• C. $\sqrt{15}$
• D. $1$

Answer 1

Answer: (C)

$\sqrt{15}$

$x^2+y^2-12x+35=0$ ........ (i)
$x^2+y^2+4x+3=0$ ........ (ii)
Equation of radical axis of circles (i) and (ii) is
$-16x+32=0\Rightarrow x=2$
It intersects the joining the centres, i.e., $y=0$ at the point $(2,0)$
$\therefore$ Required radius $=\sqrt{4-24+35}=\sqrt{15}$ (length of tangent from $(2,0)$