When the coordinate axes are rotated about the origin through an angle $\frac{\pi}{4}$ in the positive direction, the equation $a x^2+2 h x y+b y^2=c$ is transformed to $25 x^2+9 y^2=225$, then $(a+2 h+b-\sqrt{c})^2=$

$y-x=0$ is the equation of a side of a $\triangle A B C$. The orthocentre and circumcentre of the $\triangle A B C$ are respectively $(5,8)$ and $(2,3)$. The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then, the radius of the circumcircle of the triangle is

Two families of lines are given by $a x+b y+c=0$ and $4 a^2+9 b^2-c^2-12 a b=0$. Then, the line common to both the families is

Two non-parallel sides of a rhombus are parallel to the lines $x+y-1=0$ and $7 x-y-5=0$. If $(1,3)$ is the centre of the rhombus and one of its vertices $A(\alpha, \beta)$ lies on $15 x-5 y=6$, then one of the possible values of $(\alpha+\beta)$ is