The locus of the centre of the circles which touch both the circles $x^2+y^2=a^2$ and $x^2+y^2=4ax$ externally is

Let $P$ and $T$ be the subsets of $XY$ - plane defined by

$P=\left\{(x, y): x>0, y>0\right.$ and $\left.x^2+y^2=1\right\}$

$T=\left\{(x, y):x>0, y>0\right.$ and $\left.x^8+y^8<1\right\}$

Then, $P\cap T$ is