If one of the lines represented by $a x^2+2 h x y+b y^2=0$ bisects the angle between the positive coordinates axes, then

From a point $P$ on the circle $x^2+y^2=4$, two tangents are drawn to the circle $x^2+y^2-6 x-6 y+14=0$. If $A$ and $B$ are the points of contact of those lines, then the locus of the centre of the circle passing through the points $P$, $A$ and $B$ is

If the product of the lengths of the perpendicular drawn from the ends of a diameter of the circle $x^2+y^2=4$ on the line $x+y+1=0$ is maximum, then the two ends of that diameter are

If the intercept made by a variable circle on the X -axis and $Y$-axis are 8 and 6 units respectively, then the locus of the centre of the circle is