The family of straight lines $4ax + 3by + c = 0$ such that $a + b + c = 0$ (where a, b, c are real constants) are concurrent at the point...

If two lines represented by $x^2 - (1 + \sqrt{3})xy + \sqrt{3}y^2 = 0$ make angles $\alpha$ and $\beta$ with the X-axis, then $\tan(\alpha + \beta)$ is...

A straight line L passes through the point of intersection of the lines $x - y + 1 = 0$ and $2x + y - 7 = 0$. If L intersects the positive x-axis at $A(a, 0)$ and the positive y-axis at $B(0, b)$, then the minimum area of the triangle $OAB$ (where $O$ is the origin) is ....

If the combined equation of angle bisectors of the lines $x^2 - 2pxy - y^2 = 0$ is $x^2 - 2qxy - y^2 = 0$, then which of the following is true?