If the radical axis of the circles $x^2+y^2+2 \alpha x+2 \beta y+c=0$ and $x^2+y^2+\frac{3}{2} x+4 y+c=0$ touches the circle $x^2+y^2+2 x+2 y+1=0$, then $4 \alpha \beta-8 \alpha-3 \beta+10=$

If the four points $A, B, C, D$ in the Argand plane represented respectively by the complex numbers $2+i, 4+3 i, 2+5 i, 3 i$ lie on a circle, then the centre of the circle is

The centre and radius of the circumcircle of the triangle formed by the lines $2 x+3 y=10, y=x$ and the $X$-axis are respectively.

If the straight lines $3 x-4 y+4=0$ and $6 x-8 y-7=0$ are the tangents to the same circle, then the area of that circle (in square units) is