Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 2: INTRODUCTORY EXERCISE 2.2

The distance between the lines $4x+3y=11$ and $8x+6y=15$ is

A line passes through $\left(2,2\right)$ and is perpendicular to the line $3x+y=3,$ its $Y$-intercept is 

If the points $\left(1,2\right)$ and $\left(3,4\right)$ were to be on the opposite side of the line $3x-5y+a=0$, then :

The lines $y=mx, y+2x=0, y=2x+k$ and $y+mx=k$ form a rhombus if $m$ equals :

Are the points $\left(3,4\right)$ and $\left(2,-6\right)$ on the same or opposite sides of the line $3x-4y=8$

If the points $\left(4,7\right)$ and $\left(\cos \theta ,\sin \theta \right)$, where $0<\theta <\pi$, lie on the same side of the line $x+y-1=0$, then prove that $\theta$ lies in the first quadrant.

Find the equations of lines parallel to $3x-4y-5=0$ at a unit distance from it.

A line '$L$' is drawn from $P\left(4,3\right)$ to meet the lines $L_1:3x+4y+5=0$ and $L_2:3x+4y+15=0$ at point $A$ and $B$ respectively. From '$A$' a line, perpendicular to $L$ is drawn meeting the line $L_2$ at $A_1.$ Similarly from point '$B$' a line, perpendicular to $L$ is drawn meeting the line $L_1$ at $B_1.$ Thus a parallelogram $A{A}_{1}B{B}_1$ is formed. Find the equation(s) of '$L$' so that the area of the parallelogram $A{A}_{1}B{B}_1$ is least.