Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 1: INTRODUCTORY EXERCISE 3.1

The lines given by the equation $\left(2y^2+3xy-2x^2\right)\left(x+y-1\right)=0$ form a triangle which is :

Area of the triangle formed by the lines $y^2-9xy+18x^2=0$ and $y=9$ is:

If one of the lines of the pair $a{x}^2+2hxy+b{y}^2=0$ bisects the angles between positive directions of the axes, then $a,b$ and $h$ satisfy the relation

If the slope of one of the lines given by $a^2{x}^2+2hxy+b^2{y}^2=0$ be three times of the other, then $h$ is equal to :

Find the separate equations of two straight lines whose joint equation is $ab\left(x^2-y^2\right)+\left(a^2-b^2\right)xy=0$.

Find the co-ordinates of the centroid of the triangle whose sides are $12x^2-20xy+7y^2=0$ and $2x-3y+4=0$

If the lines $a{x}^2+2hxy+b{y}^2=0$ be two sides of a parallelogram and the line $lx+my=1$ be one of its diagonal, show that the equation of the other diagonal is $y\left(bl-hm\right)=x\left(am-hl\right)$.

Find the condition that the line $2x+y=0$ coincides with one of the lines given by $a{x}^2+2hxy+b{y}^2=0$.