If the point $(2, -3)$ lies on the curve $kx^2 - 3y^2 + 2x + y - 2 = 0$,then $k$ is equal to:

What type of conic section is represented by the equation $13x^2 - 18xy + 37y^2 + 2x + 14y - 2 = 0$?

The equation $x^2 + 4xy + y^2 + 2x + 4y + 2 = 0$ represents

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

Let $C$ be a curve $ax^2+2hxy+by^2+2gx+2fy+c=0$ in a Cartesian plane. By rotating the coordinate axes through an angle $\frac{\pi}{4}$ in the positive direction,if the transformed equation of $C$ is $Y^2+XY-X=0$,then $(h^2-ab)-2gf=$

$A$ 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 $^{\circ}$)