The condition that the lines joining the origin to the points of intersection of the two curves $x^2+y^2+g x+c=0, x^2+y^2+2 f y-c=0$ are at right angles, is

If $\alpha$ represent the square of the distance between the origin and the point of intersection of the lines $x^2-y^2-x+3 y-2=0$ and $\beta$ represent the product of the perpendicular distances from the origin on the pair of lines, then $\alpha \beta=$

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 $b^a r^a=$

From a point $P$ on the circle $x^2+y^2-4 x-6 y+9=0$, a pair of tangents $P Q$ and $P R$ are drawn touching the circle $x^2+y^2-4 x-6 y+12=0$ at $Q$ and $R$. If $C$ is the centre of the concentric circles, then the area of the $\triangle C Q R$ (in sq. units) is