The curve $16x^2 + 8xy + y^2 - 74x - 78y + 212 = 0$ represents:

If the chord through $(1, -2)$ cuts the curve $3x^2 - y^2 - 2x + 4y = 0$ at $P$ and $Q$,then the angle subtended by $PQ$ at the origin is (in $^{\circ}$)

The point to which the origin is to be shifted to remove the first degree terms from the equation $2x^2+4xy-6y^2+2x+8y+1=0$ is

$A$ chord through the point $(1,-2)$ cuts the curve $3x^2-y^2-2x+4y=0$ at $P$ and $Q$. If $PQ$ subtends an angle $\theta$ at the origin,then $\theta$ equals (in $^{\circ}$)

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed $1$,then the range of '$a$' is

To remove the $xy$ term from the second-degree equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$,the coordinate axes are rotated through an angle $\theta$. Then $\theta$ equals: