The equation of the circle passing through the points of intersection of the circles $x^2+y^2+6 x+4 y-12=0$, $x^2+y^2-4 x-6 y-12=0$ and having radius $\sqrt{13}$ is

If a point $P$ moves so that the distance from $(0,2)$ to $P$ is $\frac{1}{\sqrt{2}}$ times the distance of $P$ from $(-1,0)$, then the locus of the point $P$ is

If the parametric equations of the circle passing through the points $(3,4),(3,2)$ and $(1,4)$ is $x=a+r \cos \theta, y=b+r \sin \theta$, then $b^a r^a=$

A tangent $P T$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3}, 1)$. If a straight line $L$ which is perpendicular to $P T$ is a tangent to the circle $(x-3)^2+y^2=1$, then a possible equation of $L$ is