The angle between the lines joining the origin to the points of intersection of the straight line $y = 3x + 2$ with the curve $x^2 + 2xy + 3y^2 + 4x + 8y - 11 = 0$ is

If $L$ is a line passing through the point $(-1, 1)$ and parallel to the common line of the pairs of lines $6x^2 - xy - 12y^2 = 0$ and $15x^2 + 14xy - 8y^2 = 0$,then the equation of the pair of lines joining the origin to the points of intersection of the curve $2x^2 - xy - y^2 + x - y = 0$ and the line $L$ is

If the line $x+2y=k$ intersects the curve $x^2-xy+y^2+3x+3y-2=0$ at two points $A$ and $B$ and if $O$ is the origin,then the condition for $\angle AOB=90^{\circ}$ is

The equation of the pair of lines joining the origin to the points of intersection of $x^2+y^2=9$ and $x+y=3$ is:

The pair of straight lines joining the origin to the points of intersection of the line $y = 2\sqrt{2}x + c$ and the circle $x^2 + y^2 = 2$ are at right angles,if

Let the line $2x - 3y - 1 = 0$ intersect the curve $x^2 + 2xy + 5y^2 + 2x + 3y - 1 = 0$ at distinct points $A$ and $B$. If $O$ is the origin,then $\cos \angle AOB =$