Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 10: FILL IN THE BLANKS

Two lines are given by ${\left(x-2y\right)}^2+\lambda \left(x-2y\right)=0$. The value of $\lambda$ so that the distance between them is $3$, is

The pair of straight lines $x^2-3y^2=0$ and the line $x=a$ encloses a triangle which is

The joint equation of the lines passing through the origin and perpendicular to the line given by $2x^2-5xy+y^2=0$ is

If one of the lines $a{x}^2+2hxy+b{y}^2=0$ be the bisector of the angle between the co-ordinate axes, then ${\left(a+b\right)}^2=\dots \dots \dots ..$

Two of the straight lines given by $3x^3+3x^{2}y-3x{y}^2+d{y}^3=0$ are at right angles, if $d=$

One bisector of the angle between the lines given by $a{\left(x-1\right)}^2+2h\left(x-1\right)y+b{y}^2=0$ is $2x+y-2=0$. The other bisector is

The joint equation of the straight lines $x+y=1$ and $x-y=4$ is $x^2-y^2=\lambda$, then $\lambda =$