If the sides of a triangle $A B C$ are $2 x^2-y^2=0$, $x+y-1=0$ and the sides of another triangle $P Q R$ are $2 x^2-5 x y+2 y^2=0,7 x-2 y-12=0$, then the distance between the centroid of $\triangle A B C$ and the orthocentre of $\triangle P Q R$ is

If $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ is the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p, 0

If $P A$ and $P B$ are the tangents drawn from the point $P(1,1)$ to the circle $x^2+y^2+g x+g y-2=0$ with $C$ as the centre, then the area (in sq. units) of the quadrilateral $P A C B$ is

The point/points of intersection of the common tangents of the two circles $x^2+y^2-8 x-6 y+21=0$ and $x^2+y^2-2 y-15=0$ is/are