Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 1: INTRODUCTORY EXERCISE 2.1

The lines $x\cos \alpha +y\sin \alpha =p_1$ and $x\cos \beta +y\sin \beta =p_2$ will be perpendicular, if :

If the straight lines $ax+by+p=0$ and $x\cos \alpha +y\sin \alpha =p$ enclose an angle $\frac{\pi }{4}$ between them and meet the straight line $x\sin \alpha -y\cos \alpha =0$ in the same point, then :

The angle between the lines $2x-y+3=0$ and $x+2y+3=0$ is

The equation of a straight line passing through the point $\left(-5,4\right)$ and which cuts off an intercept of $\sqrt{2}$ units between the lines $x+y+1=0$ and $x+y-1=0$ is :

What is the value of $y$ so that the line through $\left(3, y\right)$ and $\left(2,7\right)$ is parallel to the line through $\left(-1,4\right)$ and $\left(0,6\right)$?

A straight line is drawn through the point $P\left(2,2\right)$ and is inclined at an angle of $30°$ with the $x$-axis. Find the co-ordinates of two points on it at a distance $4$ from $P$ on either side of $P$.

A line is such that its segment between the straight lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5).$ Obtain its equation.

The side $AB$ and $AC$ of a $\Delta ABC$ are respectively $2x+3y=29$ and $x+2y=16$. If the mid-point of$BC$  is $\left(5,6\right)$, then find the equation of $BC$.