If $I_{1,}{I}_{2,}{I}_3$  are the intercepts on x-axis, y-axis, $y=x$  with respect to $x^2+y^2+4x+2y-20=0$  then

$x^2+y^2+4x+2y-20=0$ , $C=\left(-2,-1\right)$  , $r=\sqrt{4+1+20}=5$

 $I_1=x-\mathrm{int}ercept$ $=2\sqrt{g^2-c}$ $=2\sqrt{4+20}=2\sqrt{24}=4\sqrt{6}$

 $I_2=y-\mathrm{int}ercept$ $=2\sqrt{f^2-c}$ $=2\sqrt{1+20}=2\sqrt{21}=\sqrt{84}$

 $d={\perp }^{re}$ distance from $\text{'}C\text{'}$  to $x-y=0$  $=\frac{\left|-2+1\right|}{\sqrt{2}}=\frac{1}{\sqrt{2}}$

$I_3=length$ $2\sqrt{r^2-d^2}=2\sqrt{25-\frac{1}{2}}$ $=2\sqrt{\frac{49}{2}}$ $=7\sqrt{2}$ $=\sqrt{98}$ ,

 $I_3>I_1>I_2$ .