The opposite vertices of a square are $(1, 2)$ and $(3, 8)$. Then,the equation of the diagonal of the square passing through the point $(1, 2)$ is:

The equation of a given straight line is $\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}=\gamma$. If the equation of the line perpendicular to the given line and passing through $(\alpha, \beta)$ is $\frac{x}{a}+\frac{y}{b}=1$,then $\frac{b}{a}$ is equal to

The equation of the line passing through the point $(-3, 1)$ and bisecting the angle between the coordinate axes in the second quadrant is:

The straight line passing through $(-3, 6)$ and the midpoint of the line segment joining the points $(4, -5)$ and $(-2, 9)$ has an inclination of:

Suppose a line makes an angle of $120^{\circ}$ with the positive direction of $X$-axis. If the length of the perpendicular from the origin to that line is $4$,then the equation of the line is

The line passing through $\left(-1, \frac{\pi}{2}\right)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is: