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

The perpendicular distance from the point $(1, \pi)$ to the line joining $(1, 0^{\circ})$ and $(1, \frac{\pi}{2})$ (in polar coordinates) is

The number of straight lines that can be drawn through the point $(-3, 4)$ which are at a distance of $5$ units from the point $(2, -8)$ is

If $(\sin \theta, \cos \theta)$ and $(3, 2)$ lie on the same side of the line $x + y = 1$,then $\theta$ lies in the interval:

$O(0,0), B(-3,-1), C(-1,-3)$ are vertices of a triangle $OBC$. $D$ is a point on $OC$ and $E$ is a point on $OB$. If the equation of $DE$ is $2x + 2y + \sqrt{2} = 0$,then the ratio in which the line $DE$ divides the altitude of the triangle $OBC$ from $O$ to $BC$ is:

For an integer $K$,if the point $P(K^2, K+1)$ and the origin $O(0,0)$ lie in the same region between the lines $x+2y-5=0$ and $3x-y+1=0$,then the possible number of such points $P$ is