What is the length of the perpendicular from the point $(3, 4)$ to the line $3x + 4y + 10 = 0$?

On which side of the line $7x + 5y - 9 = 0$ do the points $(3, 4)$ and $(-9, 6)$ lie?

The set of all possible values of $\theta$ in the interval $(0, \pi)$ for which the points $(1, 2)$ and $(\sin \theta, \cos \theta)$ lie on the same side of the line $x+y=1$,is . . . . . . .

The distance between the two parallel lines $y = 2x + 7$ and $y = 2x + 5$ is:

Statement-$1$: There is one line through $A(4, -5)$ such that its distance from $B(-2, 3)$ is $12$.
Statement-$2$: $AB = 10$.

If the perpendicular distances from the points $(2, 3)$,$(4, a)$ and $(\alpha, \beta)$ to the line $3x + 4y - 3 = 0$ are equal and $4\alpha - 3\beta + 1 = 0$,then the sum of all possible values of $a$,$\alpha$,and $\beta$ is: