Question

The length of the common chord of
$x^2+y^2+2x+3y+1=0$, $x^2+y^2+4x+3y+2=0$ is

• A. $\sqrt{2}$
• B. $2$
• C. $2\sqrt{2}$
• D. $4$

Answer 1

The correct option is C $2\sqrt{2}$

$x^2+y^2+4x+3y+2=0$

radius $=\sqrt{4+\frac{9}{4}-2}$

$=\sqrt{2+\frac{9}{4}}$

$==\frac{\sqrt{17}}{2}$

$x^2+y^2+2x+3y+1=0$

radius $=\sqrt{1+\frac{9}{4}-1}$

$=3/2$

$O{o}^{\prime }=1$

$Mn=1/2$

$O{P}^2=P{m}^2+O{m}^2$

$\frac{9}{4}=P{m}^2+\frac{1}{4}\Rightarrow P{m}^2\frac{8}{4}\Rightarrow 2\Rightarrow Pm=\sqrt{2}$

$PQ=2\sqrt{2}$