Amit M Agarwal Solutions for Chapter: Straight Line and Pair of Straight Lines, Exercise 6: Entrances Gallery

The value of $k$ such that the lines $2x-3y+k=0$, $3x-4y-13=0$ and $8x-11y-33=0$ are concurrent is 

The equation of one of the lines parallel to $4x-3y=5$ and at a unit distance from the point $\left(-1,-4\right)$ is

A line has slope $m$ and $y$ intercept $4.$ The distance between the origin and the line is equal to

The distance of the point $\left(1,2\right)$ from the line $x+y+5=0$ measured along the line parallel to $3x-y=7$ is equal to 

A line through the point $A\left(2,0\right)$ which makes an angle of ${30}^{°}$ with the positive direction of  $X$-axis is rotated about $A$ in clockwise direction through an angle of ${15}^{°}$. Then, the equation of the straight line in the new position is

The number of points on the line $x+y=4$ which are unit distance apart from the line $2x+2y=5$ is

The slopes of the lines which makes an angle ${45}^{°}$ with the line $3x-y=-5$ are

The vertices of a triangle are $A\left(3,7\right), B\left(3,4\right)$ and $C\left(5,4\right)$. The equation of the bisector of the $\angle ABC$ is