Which of the following equations does not represent a hyperbola?

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

The centre of the conic represented by the equation $2x^2 - 72xy + 23y^2 - 4x - 28y - 48 = 0$ 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:

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 $^{\circ}$)

To eliminate the $xy$ term from the second-degree equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$,the axes are rotated by an angle $\theta$. What is the value of $\theta$?