Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 10: Multiple Choice II

The area of the triangle is $5.$ Two of its vertices are $(2, 1)$ and $(3, -2)$ the third vertex lies on $y=x+3$ then coordinate of third vertex is

If the lines $x-2y-6=0,3x+y-4=0$ and $\lambda x+4y+{\lambda }^2=0$ are concurrent, then:

Equation of a straight line passing through the point of intersection of $x-y+1=0$ and $3x+y-5=0$ are perpendicular to one of them is:

If the lines $ax+by+c=0, bx+cy+a=0$ and $cx+ay+b=0$ are concurrent $\left(a+b+c\ne 0\right)$ then:

Consider the straight lines $x+2y+4=0$ and $4x+2y-1=0$. The line $6x+6y+7=0$ is :

Two roads are represented by the equations $y-x=6$ and $x+y=8$. An inspection bungalow has to be so constructed that it is at a distance of $100$ from each of the roads. Possible location of the bungalow is given by:

If $\left(a,b\right)$ be an end of a diagonal of a square and the other diagonal has the equation $x-y=a$, then another vertex of the square can be:

Let $L_1\equiv ax+by+a\sqrt[3]{b}=0$ and $L_2\equiv bx-ay+b\sqrt[3]{a}=0$ be two straight lines. The equations of the bisectors of the angle formed by the loci whose equations are ${\lambda }_1{L}_1-{\lambda }_2{L}_2=0$ and ${\lambda }_1{L}_1+{\lambda }_2{L}_2=0,{\lambda }_1$ and ${\lambda }_2$ being non-zero real numbers, are given by: