Any circle passing through the point of intersection of the lines $x + \sqrt{3}y = 1$ and $\sqrt{3}x - y = 2$ intersects these lines at points $P$ and $Q$. The angle subtended by the arc $PQ$ at its centre is- ............. $^o$

$A$ stick of length $10$ units rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is:

The locus of a point which moves such that the sum of the squares of its distances from the sides of a square of side length $1$ is $9$,is

Let the circle $x^{2}+y^{2}=4$ intersect the $x$-axis at the points $A(a,0), a>0$ and $B(b,0)$. Let $P(2 \cos \alpha, 2 \sin \alpha), 0 < \alpha < \frac{\pi}{2}$ and $Q(2 \cos \beta, 2 \sin \beta)$ be two points such that $(\alpha - \beta) = \frac{\pi}{2}$. Then the point of intersection of $AQ$ and $BP$ lies on:

The locus of the vertex $A$ of a triangle $ABC$,where the base $BC$ is fixed and the perimeter of the triangle is constant,is

The locus of a point which moves in such a way that its distance from $(0,0)$ is three times its distance from the $x$-axis is given by: