The equation $14x^2 - 4xy + 11y^2 - 44x - 58y + 71 = 0$ represents

The lines $y = -\frac{3}{2} x$ and $y = -\frac{2}{5} x$ intersect the curve $3x^2 + 4xy + 5y^2 - 4 = 0$ at the points $P$ and $Q$ respectively. The tangents drawn to the curve at $P$ and $Q$:

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 $^{\circ}$)

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$,the point to which the origin is to be shifted is:

If the equations $x=t^2+t+1$ and $y=t^2-t+1$ represent a curve $C$ with parameter $t$,then the Cartesian equation of $C$ is

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