If the angle made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with X-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

The area of a triangle formed by a line with the coordinate axes is $49$ sq. units. If the perpendicular drawn from the origin to this line makes an angle of $45^\circ$ with the positive X-axis, then the equation of line is....

If the equation $16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0$ represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

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...