Vinod Singh and Shweta Pawar Solutions for Chapter: Straight Line, Exercise 3: Competitive Thinking

An equation of a line whose segment between the coordinate axes is divided by the point $\left(\frac{1}{2},\frac{1}{3}\right)$ in the ratio $2:3$ is

If the portion of a line intercepted between the coordinate axes is divided by the point $(2,-1)$ in the ratio $3:2,$ then the equation of that line is

If the line $px-qy=r$ intersects the co-ordinate axes at $(a,0)$ and $(0,b)$, then the value of $a+b$ is equal to

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 $(1,5)$, then its equation is

The point $(-4,5)$ is the vertex of a square and one of its diagonals is $7x-y+8=0$. The equation of the other diagonal is

For what values of $a$ and $b,$ the intercepts cut off on the coordinate axes by the line $ax+by+8=0$ are equal in length but opposite in sign to those cut off by the line $2x-3y+6=0$ on the axes?

The equation of a straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is

The equation of a line passing through the point $(1,2)$ and perpendicular to the line $x+y+1=0$ is