Embibe Experts Solutions for Chapter: Pair of Straight Lines, Exercise 1: Maharastra Board-2018

If the sum of the slopes of the lines represented by $x^2+kxy-3y^2=0$ is twice their product, then the value of $\text{'}k\text{'}$ is 

Show that the equation $2x^2+xy-y^2+x+4y-3=0$ represents a pair of straight lines.

If the angle between the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is equal to the angle between the lines $2x^2-5xy+3y^2=0$, then show that $100\left(h^2-ab\right)=(a+b{)}^2$.

Find $\text{'}p\text{'}$ and $\text{'}q\text{'}$ if the equation $p{x}^2-8xy+3y^2+14x+2y+q=0$ represents a pair of perpendicular lines.

Find the angle between the lines represented by $3x^2+4xy-3y^2=0$

Prove that a homogeneous equation of degree two in $x$ and $y$ i.e. $a{x}^2+2hxy+b{y}^2=0$ represents a pair of lines passing through the origin, if $h^2-ab\ge 0$.