Consider the point $P(\alpha, \beta)$ on the line $2 x+y=1$. If the $P$ and $(3,2)$ are conjugate points with respect to the circle $x^2+y^2=4$, then $\alpha+\beta$ is equal to

If $(1,3)$ is the mid-point of a chord of the circle $x^2+y^2-4 x-8 y+16=0$, then the area of the triangle formed by that chord with the coordinate axes is

If the circles $x^2+y^2+2 \alpha x+2 y-8=0$ and $x^2+y^2-2 x+a y-14=0$ intersect orthogonally, then the distance between their centres is

If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of $x^2+y^2+2 x+2 y-5=0$ contains no liner terms is