Slope of a Line

The vertices of a triangle $∆OBC$ are $O \left(0, 0\right), B\left(-3, -1\right), C\left(-1, -3\right)$ find the equation of the line parallel to $BC$ and intersecting the sides $OB \& OC$, whose perpendicular distance from the point $\left(0, 0\right)$ is half.

Points $P\left(-3,2\right), Q\left(9,10\right) \text{and} R\left(\alpha ,4\right)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S.$ If $S$ lies on the line $2x-ky=1,$ then $k$ is equal to $?$

If the lines $y=3x+1$ and $2y=x+3$ are equally inclined to the line $y=mx+4$, then $m=$

Let $B\left(1,-3\right)$ and $D\left(0,4\right)$ represent two vertices of rhombus $ABCD$ in $\left(x,y\right)$ plane, then coordinate of vertex $A$ if $\angle BAD=60°$ can be equal to

If $\theta$ is the acute angle between the lines $\frac{x}{a}+\frac{y}{b}=1,\frac{x}{b}+\frac{y}{a}=1$ then $\sin \theta =$

For $\alpha \in \left[0,\frac{\pi }{2}\right]$, the angle between the lines represented by $\left[x\cos \theta -y\right]\left[\left(\cos \theta +\tan \alpha \right)x-\left(1-\cos \theta ·\tan \alpha \right)y\right]=0$ is

The diagonals of a parallelogram $ABCD$ are along the lines $x+3y=4$ and $6x-2y=7$. Then ABCD must be a 

The lines $p\left(p^2+1\right)x-y+q=0$ and ${\left(p^2+1\right)}^{2}x+\left(p^2+1\right)y+2q=0$ are perpendicular to a common line for

Find the angle of inclination of the straight line whose slope is $\frac{1}{\sqrt{3}}$

If measured in clockwise direction then the inclination is positive.

The inclination of a line parallel to Y-axis or the Y-axis itself is _____ degrees.

Find the inclination of a line $x=3$.

Find the inclination of a line $x=2$.

Find the inclination of a line $y=5$.

Find the inclination of a line $y=3$.

Find the inclination of a line $y=2$.

The angle between the straight lines $3x+4y+9=0$ and $x-7\mathrm{y}-22=0$ is

The perpendicular bisector of line segment joining the points $P(1,4)$ and $Q(k,3)$ has $y$ intercept  $-4.$ Then a possible value of $k$ among the following is $\_\_\_$

Find the acute angle between the lines $7x-4y=0\text{ and }3x-11y+5=0$.