Consider the two curves $y = 2x$ and $x^2 - xy + 2y^2 = 28$. The absolute value of the tangent of the angle between the two curves at the points where they meet is:

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

$A$ straight line through the point $(3, -2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If it intersects the $X$-axis, then its equation will be

$A$ line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2x-y+3=0$. If $L$ makes an acute angle with the positive $X$-axis in the anticlockwise direction,then the $Y$-intercept of the line $L$ is:

The equation of a line making an angle $60^{\circ}$ with the line $x+y-3=0$ and passing through the point $(1,1)$ is

What are the equations of the two lines passing through the point $(7, 9)$ and making an angle of $60^{\circ}$ with the line $x - \sqrt{3}y - 2\sqrt{3} = 0$?