The equation of the tangent to the circle x² +y² +4x-4y+4 = 0 which make equal intercepts on the positive coordinates, is

For the circle $x^2+y^2+4x-4y+4=0$, centre is (-2,2), radius $=\sqrt{4+4-4}=2$ Equation of a line having equal intercepts on the positive axes is $x+y+k=0,k<0$

$x+y+k=0,k<0$ is tangent to the circle $\Rightarrow \frac{|-2+2+k|}{\sqrt{2}}=2$

$\Rightarrow k=\pm 2\sqrt{2}\Rightarrow k=-2\sqrt{2}(\because k<0)$

$\therefore$  Required tangent equation is $x+y-2\sqrt{2}=0$