The angle between the lines joining the origin to the points of intersection of the line $x\sqrt{3} + y = 2$ and the curve $x^2 + y^2 = 4$ 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

The distance between the lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ is

The area (in sq. units) of the triangle formed by the lines $x^2-3xy+y^2=0$ and $x+y+1=0$ is

The line $x+2y-c=0$ meets the curve $x^2+y^2-3x-6y+3=0$ at two points $P$ and $Q$ and $\angle POQ = \frac{\pi}{2}$,where $O$ is the origin. Then $2c^2-15c =$

The equation of the pair of straight lines joining the origin to the points of intersection of the curve $x^2 + y^2 = 4$ and the line $y - x = 2$ is